Bitcoin is a digital network created/discovered by Satoshi Nakamoto on 31st October 2008 with the release of the white paper published to a cryptocurrency mailing list.
The first open source Bitcoin software client was released on 9th January 2009, with Hal Finney as the first human receiver of a Bitcoin transaction.
Bitcoins are the monetary units that humans can send to each other peer to peer without a trusted 3rd party via the Bitcoin network. Satoshi's are units of Bitcoins, there are 100,000,000 (one hundred million) Satoshi's per Bitcoin and there will only ever be 21 million Bitcoins (20,999,999.97).