SMS is voice, so there can't be an SMS client that uses data, any more than there can be a canary that's a fish.
Current versions of Android have Hangouts, so that would work, but it's not data, it goes via the voice channel. Since it's SMS, it bills as text.
Any app that sends messages by internet (IOW, doesn't bill as text) requires that the recipient have an app that can receive the data. The first 3 apps that predator mentioned require the same app on the other end. Textra and hangouts are SMS (billed as text).
Google Voice is about the only one that will send an SMS via data. (You'll receive it as a notice that you have a voicemail.) Note that if your GV number is forwarded to one or more cellphones, any texts received on your GV number will be sent to the phone(s) as texts, and you'll be billed for them if you're billed for incoming texts.
Email is pretty fast these days, so you can "chat" using email, which is data, and no one needs any special email app - any email app will work (even on iPhones - Apple didn't invent its own email, the way it invented its own texting.)