Foreclosure vs. Short Sale: Is this correct?

It depends on what state you live in and what type of mortgage you had. Banks holding second mortgage debt can often chased the borrower for a long time.

In a short sale, the bank agrees to accept the amount offered in the purchase agreement in settlement of the mortgage balance. They will not come back and try to collect, however they usually will send the borrower a 1099-C (for cancellation of the remaining debt) which then becomes income to the borrower that has to be reported to the IRS and taxes paid on the amount.

A foreclosure is simply stopping paying and walking away (or getting evicted). In this, the bank has not voluntarily agreed to accept a lower amount. If you are in a non-recourse state, then the bank probably cannot chase the borrower. If you are in a recourse state, the bank can chase the borrower. In either case, the 1099-C probably also applies.

The only way I know to get through a foreclosure without subsequent chasing is to file bankruptcy first (before foreclosure) but anyone contemplating that needs to talk with a skilled bankruptcy attorney first.

If there are no assets to go after it's not worth the time or energy, let alone attorney fees.

NO. In some states the lender can sue you for their loss.