I thought about trying to write it out, but here's a simple version, quoted from online-poker-insider:
"In a Freeze Out poker tournament the structure is such that all players start with a specific number of chips and do not have the option to replenish or add to this chips. That means there are no rebuys allowed and no add-ons.
The tournament is over when all players but one have been eliminated, or frozen out, and one player is left with all the chips. The most important aspect of a freeze out tournament is that as players are knocked out the tables are combined and broken down. This is in contrast to a shootout structure where the tables are not combined and each table produces a "winner" who then goes on to a new table once all the players at his table are eliminated."
Freezeouts are often called 'elimination' tournaments, the most common found online. In many BnM
casinos, shootouts have become common but are often a shootout/freezeout hybrid with a time limit where tables are combined based on elimination but end at a specific blind level or time limit and the winners are determined by chip stack at the end of the time allotment.
I've talked with several poker room people and their opinion of calling elimination tourneys 'shootouts' is that the term shootout has more 'excitement' appeal to players than 'freeze out' or 'eliminate'. It's all about attracting players, so the terms get a bit bent over time.