Exactly. The first two are promises, so-called IOUs. If I send you $5 from my bank account, I will have only moved a promise. Only if we met in real life and I handed you over $5 in cash, we'd have actually accomplished a transaction of $5 without IOUs, intermediaries, promises, trust in general. Only then we would have moved dollars - the asset. In any other way, we'd have moved a liability.

We use electronic cash for the same reason we use cash to settle transactions. Censorship resistance, privacy, lower costs, financial sovereignty.