From Wikipedia:
If you have to take the servers offline to apply it, then it's not a hotfix, it's a patch or an update. I've run live-ops for games and I have never heard of a hotfix that involved any downtime beyond maybe a restart.A hotfix or quick-fix engineering update (QFE update) is a single, cumulative package that includes information (often in the form of one or more files) that is used to address a problem in a software product (i.e., a software bug).[1] Typically, hotfixes are made to address a specific customer situation.
The term "hotfix" originally referred to software patches that were applied to "hot" systems; that is, systems which are live, currently running, and in production status rather than development status.