I’m $10 short = I have $10 less than I need. I'm out $100 = I paid that sum of money and now I feel like I lost it. Not happy at all.

It can mean "I'm short 8K" as you suggest. More often, though, it means you've lost 8K somehow. For instance, you've played poker all night and lost 8K. You can say "I'm out 8K on the night". Another example is if you've lost on some transaction. You bought a car for 20k, but had to sell it in a hurry the next week for only 12k. You could say "I'm out 8k" as you incurred a loss of 8K on the quick trade.