Crypto ⇄ external method (FIAT)
One side puts up crypto (protected by the escrow) and the other pays through an external method (bank transfer, etc.). Once the payment is confirmed, the crypto is released.
Crypto ⇄ crypto (escrow swap)
Both sides put up crypto, even on different networks. The escrow manages one wallet per side and per network, and releases each one's share once both deposits are in. It's a cross-chain swap with an arbiter.
In every case you choose the network for each side. Check out Supported networks and currencies to understand why the network matters.