blockchain is simply a chain of blocks and you can refer to it as "the database". as a result you don't implement the database, you implement the protocol. Bitcoin is the implementation of a different set of protocol rules where as Ethereum is the implementation of another different set of protocol rules.

now each cryptocurrency has something we refer to as "coins" which have the same name as the project. for example Bitcoin coins are called bitcoin, Litecoin coins litecoin and Ethereum coins Ether. of course in ethereum it is not a "coin" per se, it is a token and is used as fuel for smart contracts. but the concept is similar.