Does Electrum use Bitcore Apis as it's backend? Does Electrum use Bitcore Apis as it's backend or not? 

If not, then what is the purpose of developing Electrum when Bitcore Apis provides all the features Electrum has (like HD wallets and master seeding)?
Electrum uses the electrum-server backend (electrumx is a newer variant)

In fact, electrum actually predates bitcore by about 2 years.

As to why there are multiple implementations of similar APIs and softwares, the answer is really "Why node?". Even the bitcoin node software has multiple implementations (Bitcoin Core and btcd, for instance). 

This is a very open source friendly space, and it is generally actively encouraged to have multiple approaches to a problem.