Correct on one part of your question.

Tax deed sales in FL will clear all existing liens other than governments as long as they are noticed before the sale properly.

Foreclosure sales only clear what is junior to their lien position. So a 2nd position mortgage foreclosing wouldn't clear the 1st mortgage, but a 1st position mortgage foreclosing would clear the other mortgage.

The HOA or condo association foreclosure wouldn't clear either of them when they foreclose. It's a song and dance of liens, and lien positions that you need to learn to make money with these foreclosure auctions.

In FL, tax deed sales do NOT clear all existing liens. Each lien holder has 120 days to file a claim against surplus funds remaining after the tax deed sale. The claimants must submit supporting documentation to show what is owed to them.
AFTER 120 days, their right to monies owed is extinguished.

The same is true when a first lien files a foreclosure in a judicial state. Jr lien holders have a limited amount of time to file a claim against any surplus monies retained by the clerk.

When a 2nd lien or HOA files a foreclosure, the 1st mtg is not wiped out. The fist mtg has a right to file foreclosure against the auction bidder/new owner.

If you have the money to bid at auction, you 100% need to spend a few hundred bucks to order a good title search.