A static fire test is a test in which the (first stage) engines are ignited ("fired") but the vehicle does not launch (it remains "static"). Hence, "static fire".
A wet dress rehearsal is a simulation of a full launch processing flow. Whether or not a wet dress rehearsal includes a static fire or not depends on your exact definition of "wet dress rehearsal".
For companies that do perform a static fire during a wet dress rehearsal, you might ask yourself what the difference is between the two. The difference is the focus: a static fire mostly tests the engines and the associated plumbing. A static fire would only put the minimum amount of propellant in the tanks that is required for the static fire. (Which for Starship only takes about one second.)
A wet dress rehearsal simulates the full launch processing flow, so they would fill the tanks to flight levels. They would also simulate integration of the payload, for example.
Another term that you might hear is green run. This seems to be used by Boeing, for example, to describe a combination of wet dress rehearsal and full-duration static fire, including thrust vectoring tests, etc. So, they will simulate not only the full launch processing flow, but even the full flight itself, including firing the engines for up to 8 minutes, gimbaling the engines while firing, etc.
Note that there are different kinds of static fires. Since Starship is still in development, let's look at Falcon 9 instead:
Each Merlin engine that is built in Hawthorne is fired at least once on the horizontal test stand in McGregor.
Each Falcon 9 booster that is built in Hawthorne is test fired on the vertical test stand in McGregor with all 9 engines for the full flight duration before being shipped to Cape Canaveral or Vandenberg.
Before some, but not all flights, the fully stacked vehicle is raised on the launch pad and the booster conducts a short ~1 second static fire of all 9 Merlin 1-D engines. It seems they are now moving away from static fires in some cases and only do them when
- the booster is very new, i.e. on the first few flights,
- the booster is very old, i.e. when the booster is pushing the reuse limits,
- they swapped an engine on that particular booster,
- they had some problems with the engines in other flights directly before.
They seem to be comfortable launching without a static fire when the booster has successfully flown with those same 9 engines a couple of times already but not as often that it is pushing the limits of reuse, especially when it is only launching their own payload (Starlink) as opposed to paying customers or even human crew. They have 9 boosters that have flown 3 times or more, but only 2 that have flown 8 times and only 1 that has flown 9 times. They can be pretty confident that a booster that has flown between 3–6 times will work.