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 ecash is like a protocol build on top of bitcoin that connects via lightning? 
 Yes,

Chaumian ecash is an old version of electronic ecash for dollars that didn't work out.

"eCash", "eNuts", "eStats" are all slang for versions of chaumian blinded mints that now run on top of lightning. Fedi is one protocol, cashu is another, similar ideas, different trade offs.

Send bitcoin to a mint via lightning, get issued a near perfect private bitcoin iou you can spend and send out of bound redeemable by the mint for sats.