Like a lot of start-ups, TransferWise started with a simple idea, inspired by the frustrating personal experience of one of its founders.

Kristo Käärmann landed a job with Skype in London a decade ago but still had a savings account in his native Estonia. When he wired money home through his bank, he was surprised at the transfer cost. It was not just the bank fee that penalized him but the exchange rate the bank used to convert his pounds into euros. Käärmann's fellow Estonian in London Taavet Hinrikus was paid in euros and needed to convert his pay into pounds, so they worked out a deal using mid-market foreign exchange rates. They soon had a network of friends exchanging money informally.

"We realized it was a problem not just for Estonians in London but for everyone who's moving money internationally," said Käärmann, now TransferWise CEO.

Match up two people who need each other's currency and you avoid the bank charges and the excessive costs of foreign currency conversions. The idea spread to their circle of friends and that led Käärmann and Hinrikus to create the company in 2011.

Eight years later, TransferWise ranked No. 23 on CNBC's 2019 Disruptor 50 list and has done so by revising its business model, something many start-ups fail at. "Our peer-to-peer model was an innovative solution at the time, but as we scaled, the original model wasn't scaling with us," said Käärmann. "It took us five, six years to get to break-even," Käärmann said.

The company has grown to 1,500 employees and handles $5 billion a month in transactions across 71 countries through a smartphone app, TransferWise had reason to ditch the original system and refocus on costs.

"Our mission is money without borders – instant, convenient, transparent, and low-cost," Käärmann said.

Unlike many start-ups, TransferWise is profitable. In the year ending March 2018, the company, headquartered in London, reported a net profit of $8 million on revenue of roughly $151 million (at current exchange rates).

TransferWise's rapid growth has been fueled by one of the world's most important, and most unglamorous, money markets. The term "remittances" doesn't sound very sexy, yet last year the flow of money between individuals across national boundaries totaled $689 billion, up 8.8% from 2017, according to the World Bank. Remittances — mostly from immigrants working in wealthy nations to relatives back home — pay for schooling, weddings and funerals, put food on the table, and buy the cement blocks for the additional room.

Remittances are increasingly critical to economic activity in much of the world. Excluding China, remittances to low and middle-income countries ($462 billion) were significantly larger than foreign direct investment in 2018 ($344 billion), according to the World Bank. And the cost of remittances is high, on average 7%, but as high as 10% to certain African countries.

Western Union, which does business in 200 countries and moved $300 billion ($88 billion internationally) last year, is hardly complacent about the competition.

"It's a race and we are running very fast," said Odilon Almeida, president of Western Union Global Money Transfer.

He noted that his company's business, once practically all cash, is now 12 percent digital, paid to smartphones, mobile wallets or bank accounts.

"We think mobile first," said Almeida. "You can choose the way you pay." The company offers a mobile app in 35 countries and also handles transactions through its web site.

More from CNBC Disruptor 50

The next breakthrough in agriculture may come from outer space

The future of the $1.2 trucking market may create a better Uber

Chinese facial recognition can identify you in one second

Unlike long established rivals Western Union and Moneygram, TransferWise's business is all-digital. It doesn't bear the costs of thousands of outlets that its competitors use to pay out cash.

That approach also provides Western Union with a business that remains differentiated, serving different customer needs than TransferWise, and across a larger network. TransferWise requires customers to have bank accounts on both sides of the transaction, which eliminates a large portion of individuals looking to send or receive cash. Western Union's walk-in retail network in urban, rural and remote areas covers more than 200 countries and territories. It is a point that TransferWise concedes, for now.

"I really admire Western Union for their ability to deliver money to a blue hut in an African country," Käärmann said. "But the last mile in the next ten years will be very different from what it was in the 1990s."

His company's transfer fees are a fraction of what banks and payment agencies like Moneygram and Western Union charge. The company says the average fee a TransferWise user paid in Q1 was 0.63% of the money transferred. In the eurozone specifically, TransferWise started out charging 0.5% of the amount of a transaction; it has since lowered the charge to 0.35%.

Western Union says that the global average cost of transferring money through Western Union (including fee and FX) is approximately 5 percent of the amount being sent. The average person-to-person principal send value via Western Union in 2018 was about $300.

Western Union shares show the industry-wide pressures created by innovation: They are lower today than they were a decade ago, during what has been a period of economic expansion and broad stock market growth. Moneygram, meanwhile, as a smaller player in the industry with less money to spend on keeping up with the competition, has performed even worse. Moody's recently downgraded its credit profile and cited the difficult operating environment.

Western Union's large territory allows them to continue to charge more in many markets, while digitally they have become more competitive on pricing.

"The reality is that on the online side of the business, Western Union is more competitive, but not as competitive, as TransferWise in some corridors," said Darrin Peller, managing director at Wolfe Research and payments sector analyst.

But the digital growth comes at a cost to Western Union's profit margins.

"When it comes down to it, they have not been able to grow EPS as well as others, and the question isn't just why, but why given the backdrop of a world where remittance flows grow in mid- to high single digits?" Peller said.

Part of the answer is the incremental competition causing pricing pressure. Western Union has done well in building its digital business and bringing customers to WU.com for digital transfers, but they make a lot less money on that business than the traditional cash transfers. The competition is forcing Western Union to cannibalize its own highest margin transactions.

And the competition is at the same time forcing Western Union to spend more. "Whether it is digital wallets like Venmo and Square or TransferWise or Remitly, the innovation around technology means they have to spend a lot more money than some thought they would have to spend."

TransferWise is focused on speed in addition to low costs.

"In the last quarter the money arrived in 19% of recipients' bank accounts in less than 20 seconds," Käärmann said.

TransferWise achieves speedy results by embracing some of the tools of mainstream financial institutions. The company was the first nonbank to get its own settlement account at the Bank of England. In anticipation of Brexit, TransferWise has applied for an office in Brussels. The original peer-to-peer model has also become less important as TransferWise has developed relationships with banks around the world to manage payouts.

It has introduced a "borderless" account allowing customers to move money between 40 different currencies. Traditional banks, like France's Groupe BPCE, and digital banks, like Britain's Monzo, are incorporating the TransferWise money-transfer function into their own applications. "A few big banks that have come to the conclusion that their wire-transfer service was never a good experience for the customers," Käärmann said.

Alex Rampell, a general partner at venture capital firm Andreessen Horowitz and an investor in TransferWise, said Käärmann's determination to keep costs down for customers has been key to the success of the company. "There are companies that try to figure out how to make the most money from you, like Apple, and those trying to charge as little as possible, like Costco."

"We have proven the fees, which are often 10 times cheaper than the bank charges, actually work," Käärmann said, citing two straight years of profit.

Recent news reports indicated that TransferWise is lining up another round of investment that would set its valuation at $3.75 billion. The company would not comment on fundraising. It has raised $397 million in funding from investors, including Index Ventures, Andreessen Horowitz, Richard Branson and Paypal co-founder Max Levchin.

Rampell believes that TransferWise's focus on costs is a winning strategy. "Every month, users get a newsletter telling them the costs have been lowered in this currency or that. Who else does that?"