Eris is used for building your own block chain.
Bitcoin is one blokchain with paticular properties used for financial transactions.
Fully decentralised networks such as Bitcoin use distributed computing power to process and verify transactions broadcast upon them. The network, being aware of the history of all transactions, engages constantly in a process of automated database management and transaction verification through the voluntary provision of computing power, in a process which many blockchains call “mining”, but for Thelonious it is called “committing”.