eli5

What's the difference between connecting a wallet and signing a message to verify ownership? Is there a case where I could connect a wallet that I don't own?

/new-york by day 🗽 /latenightcrew by night :) Fan of eating tacos and bringing people together, often at the same time 🌮 oh and /untzuntz 😈

you can connect any wallet. 
https://impersonator.xyz/

connecting allows an app to request the wallet to do things but is just a wallet app level security standard that doesn’t involve using the actual key pair 

signing is your wallet doing something

yeah connecting is read only, signing is proof you can write from it

can larp as wallets to see activity/holdings in some apps

yes - if you just want to play w/ something but not verify its your account, injecting another wallet is quite nice.

you can also inject another user's wallet to see their positions & actions in a UI you're familiar with. a good of example of this might be defisaver.

frame.sh is good for watching wallets