FIRST there was a concept of a "coinbase transaction" (It was the description for the type of transaction that pays the block reward to the miner).
Then, many years later, someone formed a company that was going to be an exchange for Bitcoin. They decided that they wanted to name their company after this transaction type because it would be a familiar word to people that understood Bitcoin.
So, the name of the company is referring to the transaction type, not the other way around.
It's the same with "Blockchain".
FIRST there was the concept of a "blockchain" (It was a description for cryptographically linking blocks of data together).
Then, many years later, someone formed a company that was going to create a website that allowed users to see Bitcoin transactions. They decided that they wanted to name their company after this concept of linking blocks of data together because it would be a familiar word to people that understood Bitcoin.
So, the company/website Blockchain.info is referring to the pre-existing concept, not the other way around.