Square (NYSE:SQ) has had a ton of success with its Cash App over the last year or so. Earlier this year, third-party data indicated that Cash App downloads surpassed those of PayPal's (NASDAQ:PYPL) Venmo, a competing peer-to-peer mobile payments service.

However, despite Square's success, Venmo is growing faster than ever. "For the third quarter in a row, Venmo posted yet again another record for net new actives," PayPal CEO Dan Schulman told investors during the company's third-quarter earnings call. The accelerating user growth has led to several other positive results for PayPal, including faster payment volume growth and an increasing number of customers using its monetized services.

The Venmo app open on a phone sitting on a table of apparel.

Image source: Venmo.

PayPal's copycat products

Square's Cash App's rapid growth is tied to a string of new product releases over the last couple of years. It offered in-app bitcoin buying and selling, the ability to receive direct deposits in the app, instant transfers from the app to a checking account, and a debit card linked to the balance in the app.

PayPal has copied some of the most successful new features -- notably instant deposits and the debit card. And the copycats have been a success.

Venmo processed $1 billion in instant transfer volume from Venmo in September. By comparison, Square processed $4 billion in instant deposits in the second quarter across both merchants and consumers. So, PayPal is already close to catching up.

The Venmo card, meanwhile, saw transaction volume grow 320% month over month in September (but management doesn't provide any details on total volume). For reference, Square says Cash Card users spent $250 million in June.

The expanded functionality of the apps gives consumers more reasons to download them and more reasons to use them. Both apps also benefit from the network effect, which encourages more transaction volume on the apps from existing users as new users join. Venmo transaction volume increased 78% year over year last quarter.

Taking more monetized services

PayPal says 24% of Venmo users have participated in a monetizable action, up from 13% in May. There are three main actions Venmo monetizes: instant transfers are paid for by the user, and Venmo card and Pay with Venmo transactions are paid for by the merchant.

Instant transfer has proven popular enough that PayPal is raising the price from $0.25 per instant transfer to 1% (with a $0.25 minimum) starting next month. Square also recently increased the fee on its instant deposit feature to 1.5% from 1%.

PayPal's ability to monetize Venmo is a big part of its future. The $70 billion per year run rate of payments on Venmo is a massive drag on PayPal's take rate since the company typically doesn't collect a percentage of peer-to-peer payments. If PayPal can make up for it with ancillary services like instant transfers, it will offset the cost of operating the service.

PayPal is also seeing good adoption of its other monetized Venmo services, including Pay with Venmo. It's partnered with several big merchants, including Uber, and management says it has a list of merchants lining up to use the service. Pay with Venmo offers a chance for PayPal to take some of the volume that's going to other payment processors and grow its market share, although it could cannibalize its core business.

PayPal hasn't come up with very original ways to monetize Venmo, but it's hard to argue with the results it's seeing. Even as Square shows excellent growth of its Cash App, Venmo has proven its copycat strategy is working to stave off the competition -- and make some money doing it.

Adam Levy has no position in any of the stocks mentioned. The Motley Fool owns shares of and recommends PayPal Holdings and Square. The Motley Fool has the following options: short January 2019 $82 calls on PayPal Holdings and short January 2019 $80 calls on Square. The Motley Fool has a disclosure policy.