Definition
The Stratum protocol defines how mining hardware communicates with mining pools. Stratum v1 (the current standard) uses a simple JSON-RPC over TCP connection. The pool sends work to the miner, and the miner submits shares (valid partial solutions) back to the pool.
Stratum v2 is an upgraded version that adds binary encoding (more efficient), encryption (privacy), and crucially, the ability for miners to construct their own block templates rather than accepting templates from the pool. This last feature is important for mining decentralization, as it prevents pools from censoring transactions.
In Simple Terms
The protocol miners use to communicate with pools. Stratum v2 adds encryption and miner-selected transactions.
The communication protocol used between miners and mining pools. Stratum v1 is the current standard; Stratum v2 adds encryption and allows miners to select their own transactions.