eBay's (NASDAQ:EBAY) PayPal, which is dealing with rising competition from Amazon (NASDAQ:AMZN) and spin-off rumors, now faces a new threat -- Square's updated Cash app for mobile devices.

Square's new Cash app lets users send cash via messages, adds notes to payments, and introduces a referral system that gives users $1 for each newly invited user. The update also imports address books, profile pictures for user accounts, and a unified email and phone contact list for easier payments. Push notifications are provided for incoming transfer requests. In other words, Cash is aiming to become the WhatsApp of mobile payments.

Square's new Cash app. Source: iTunes.

Let's take a closer look at Square's new strategy and how it could affect eBay and PayPal in the future.

Square vs. PayPal
Square's first product was a card-swiping dongle and app, the Square Reader, which it launched in 2010. In 2011, it added Card Case and Register. Card Case let users link credit cards to their mobile devices to make quick payments, receive receipts, and find special offers from merchants. Register converted an iPad into a full-featured cash register. Square's strategy disrupted the market for traditional point of sale (POS) systems, which can cost up to $1,500 each.

PayPal, which eBay acquired for $1.5 billion in 2002, grew into a giant as eBay's payment system. PayPal expanded to other e-commerce sites and rose in popularity, since it was often easier to simply pay with an email address instead of reentering credit card information on websites. Noticing how quickly Square was growing, PayPal launched PayPal Here, its answer to Square Reader, in 2012.

Square Reader (L) and PayPal Here (R). Source: Company websites.

Opposite starting points, intersecting growth
Square grew by streamlining payments for brick-and-mortar retailers, while PayPal fed on the growth of e-commerce. Now both companies are encroaching on the other's home turf.

Last June, Square launched Market, which let its bricks-and-mortar customers easily set up online storefronts, which gave them an instant e-commerce presence. In 2012, PayPal signed deals with major retailers to add PayPal as a payment option alongside major credit cards. PayPal users could use a physical PayPal card, or enter their mobile number and pin code.

Financially, Square is still the David to PayPal's Goliath. Square reportedly processed $20 billion in payments in 2013 and is expected to generate $1 billion in revenue this year. PayPal processed $180 billion in payments and generated $6.6 billion in revenue in 2013. Both companies profit from transaction fees -- PayPal charges 2.7% per swipe, while Square charges 2.75%.

The business of mobile payments
Of PayPal's $180 billion in payments, $27 billion came from mobile platforms. PayPal's mobile payments off eBay rose 128% year over year. That growth is in line with the rapid growth of the mobile payments industry. Research firm Gartner expects worldwide mobile payment transaction values to more than triple from $235.4 billion in 2013 to $721 billion by 2017.

PayPal's app helps users find nearby stores that accept PayPal, check in, get special deals, and pay from their phones -- but it's not a social app.

PayPal's app. Source: iTunes.

What makes Square Cash so dangerous is that it organizes a user's phone book contacts into a messaging system -- similar to social messaging apps WhatsApp, WeChat, or LINE do. That snowball effect, which gathers more users with every new member, helped WhatsApp double in size from 300 million to 600 million users over the past 12 months. Square Cash is accelerating that strategy with referral bonuses, which could help it quickly gain a lot of mobile users.

Square's biggest weakness
Square's strategy is alarming, but it doesn't threaten PayPal's core business of eBay payments. However, Square could keep PayPal cornered within eBay if it gains more ground with brick-and-mortar retailers and individuals on mobile devices.

Square's big weakness is its bottom line. According to The Wall Street Journal, Square reported a loss of $100 million in 2013, wider than its loss in 2012. Four-fifths of the 2.75% Square charges merchants goes to payment networks like Visa, MasterCard, other financial institutions, and fraud prevention expenses.

Not much more is known about Square's finances, but it is clearly suffering the classic problem of young tech companies -- soaring revenue weighed down by big expenses.

A Foolish final word
Competition in mobile payments is heating up, and Square's new Cash app is a disruptive wild card, just like Card Case and Register were in the past. In the meantime, the ongoing battle between PayPal and Square could yield more innovative mobile payment products for retailers and customers in the future.

Leo Sun owns shares of Apple. The Motley Fool recommends Amazon.com, Apple, and eBay. The Motley Fool owns shares of Amazon.com, Apple, and eBay. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.