More specific, the part "Remote Procedure Calls (RPCs)"... There are also other options, like running bitcore: https://bitcore.io/guides/wallet-service/
This being said: i never recommand anybody to start using a web wallet, starting a wallet service as a novice user without any trust is a bad idear (IMHO)
If I maintain most bitcoin source as-is, other developer can make my coin's wallet with using that bitcore API?
If you clone bitcoin, your developer *should* be able to clone bitcore, changing the same parameters that were changed when cloning bitcoin...
I success cloning litecoin v0.8, but it is 4 years ago version.
Now I want to clone newest bitcoin source, 0.15.1.
But when I see it, source code position/structure changed a lot.
For example, base58.h 's "PUBKEY_ADDRESS = 35" is changed to chainparams.cpp 's "base58Prefixes[PUBKEY_ADDRESS] = std::vector
What this means and how to change key address's prefix?