- What are the similarities / differences between them?
- Which use cases are best for each network
- Are there more than these listed above?
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If you need a stable testnet with support on multiple clients go with Goerli. If you need to have conditions as close as possible to mainnet, but less stability than Goerli, choose Ropsten.
Detailed version below:
besu --network ropsten
openethereum --chain kovan
15 seconds on average
There are other (test-)networks as well, as described in this SO answer, copied here with their network id numbers:
0: Olympic, Ethereum public pre-release testnet
1: Frontier, Homestead, Metropolis, the Ethereum public main network
1: Classic, the (un)forked public Ethereum Classic main network, chain ID
2: Morden, the public Ethereum testnet, now Ethereum Classic testnet (retired)
3: Ropsten, the public proof-of-work Ethereum testnet
4: Rinkeby, the public Geth Ethereum testnet
5: Goerli, the fresh cross-client Ethereum testnet
42: Kovan, the public OpenEthereum testnet
77: Sokol, the public POA testnet
99: POA, the public Proof of Authority Ethereum network