Well there is 1 general rule when it comes to money: What is not in your hand is not yours.

Its promised to be yours so its a PROMISSARY NOTE or an IOU, but not real money. If you hold it at a safe location like offline wallet, and only you have access to it at any day or hour (given that you got internet and electricity) then it's yours.

If you keep it at a third party and they: steal it, scam it, server shuts down, glitch happense in their payment processing, their server gets hacked, or any other unpleasand thing happense, then its not your money, its only a promise, that they may or may not fill.

I heard that many online wallets dont keep 100% reserves, which is exactly what the current banking industry does, an accident waiting to happen lol Like mt gox....