I believe the two words have a bit of gray area in between them, but here's how I understand it:
If you issued a $100 invoice that is going through processing and will be paid to you in 30 days, but you owe someone $50 right now, you're illiquid.
If you have $100 long-dated bond that is currently worth $50 on the market, and you owe someone $60 right now, you are actually insolvent. Not just illiquid.
There is no gray area, just trickery. Your scenario is equivalent to saying if I have $70 in assets and $100 liabilities, then I am not insolvent if someone gifts me $30. People will not keep billions of dollars in your bank earning 0% while the rest of the world collects 4-5%.
Alternatively, if I am a bank in March 2023 and I have 70B in cash and 100B in liabilities, can I become solvent by buying these 1.5% yielding treasuries and MBS at market rate of 70 cents on the dollar and say, "don't worry, I'll have $100B in 10 years to pay everyone". Of course not.
