What specifically does Adaptor Signatures and DLEQ Proofs do, that HTLC doesn’t?

I’n aware that
• Adaptor Signatures enables XMR~BTC trading, and
• DLEQ Proofs enables XMR~ETH/ERC-20 trading.

I’ve also understood that HTLC enables cross-chain Atomic Swaps between cryptocurrencies with smart contract capabilities, and that Adaptor Signatures and DLEQ Proofs enables cross-chain Atomic Swaps between smart contract coins with non-smart contract coins.

I just don’t understand how this is done.

Is it possible for the Swaps core dev to give us some insight into these cross-chain Atomic Swaps mechanisms?