> seems like a fuzzy distinction
Not really. Insolvency is by definition time independent. If you owe more than you have, you're insolvent. It doesn't really matter if you might make enough to cover the difference in the future.
In practice, you might get away with it if no one forces the issue upon you, but that doesn't change the math of whether or not you could pay your debts.
Liquidity is different. It is time dependent by definition. Some things take time to structure, deal, and sell. You can also get away with this in practice.
They can both have similar effects when they happen, but their causes are sharply different. I have a house I can sell to cover my mortgage, but couldn't sell it in less than a couple weeks or maybe even months. Illiquid but solvent.