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 cashu ecash is a custodial iou for sats on the ln node of the mint but the tokens are bearer assets on the device 

it offers superior privacy over any other custodial LN solution

the "ecash" will typically be denominated as sats but can also be in usd

the mint can't rug an individual but could rug the whole mint 

if users are on the same mint tokens can be sent out of band by dm, text, email for free

Minibits pays any ln invoice as well

there are certainly ways to zap self custodially but minibits has amazing product fit for nostr 

send out your balance to redeem sats into self custodial ln channel on Zeus for example

 
 Ah, thanks, that was my confusion; I thought the ecash was the token being stored on the device. Didn't realize ecash was an IOU held by the mint operator. The way it's presented on the website is: "Ecash is a digital barer token that is stored on a user's device, very similar to physical cash."

https://docs.cashu.space/# 
 Yes token is on device but is only redeemable for actual lightning sats by the mint that issued it 
 If Alice has tokens issued from Minibits and sends them to Bob who uses enuts, can he redeem the tokens from Alice? He would be trying to cash in tokens that enuts did not issue. 
 Yes because Alice's ecash token would be redeemed for sats that would be paid over lightning network from minibits ln node to enuts ln node which would then issue Bob ecash tokens that are kept on his device 
 If Alice and Bob share the same mint then they can send ecash to eachother without a lightning transaction and with near perfect privacy  
 iiuc, Alice & Bob can send the bearer tokens amongst eachother intra mint with no Lightning tx but to send inter mint; the token has to be redeemed by the Alice's mint, sats sent via Lightning tx to Bob's mint, and there new bearer tokens are issued to Bob.