Mining Algorithm vs Hashing Algorithm vs Consensus algorithm?

What is the difference between a mining algorithm (ethash, dagger) vs a hashing algorithm (sha256, cekkak) vs a consensus algorithm (casper FFG, heaviest chain, etc)?

afaik hashing algorithms are responsible for the general security of blockchains like pub/priv keys and consensus algorithms are responsible for checking that everyone has the same network state before a block is added. What does a mining algorithm do and what algorithm does bitcoin use?

I haven’t been able to find a clear answer on this as I am relatively new to blockchains and don’t understand the technical docs. Thanks for the help!