Is there an API that supports different Bitcoin wallets? Is there an API that has sending and receiving functionality of different Bitcoin wallets such as Coinbase, Bitcoin wallet, etc...

Or would I have to manually incorporate each wallet API myself?
I found out about Coinkite after I posted this. I send an email to their support team asking:

"With this platform, will I be able to have a user link their wallet and be able so send bitcoins to another users wallet, regardless of what wallet they use?"

I got a response of "Yes" and they sent me a link to their docs