Sanity tests or smoke tests are black box tests that check basic assumptions of your code that must be true in all cases.
Sanity tests can be unit or sytem tests but must be deterministic.
An example of sanity tests would be that all costume implemented hash functions adhere to a certain set of criteria.
Or a Hello World program can be considered a sanity test for the development environment.
Checksums are often used to sanity test if an installation was successful.
Depending on the introspection capabilities of your language, setting up sanity test can be more or less time consuming.
Consider the hash example from before. In a language with good introspection like Python,
a test script could access the whole code and its AST to match function names to a given regex.
Doing the same in languages like C or C++ would require writing a script which partially parses and compiles segments of the code,
which is much more work.
( for performance tests as acceptance tests look here )
Performance tests are a form of sanity tests that check that the required time is not exceeded.
If you are developing a game with the target frame rate of 60 FPS,
then it makes sense to write a test to test that your game loop only takes a maximum of 1s / 60 = 0.016s = 16ms.
Performance tests should never be used to diagnose the problem, but can always serve as a warning signal, that something is wrong.
Another form of sanity tests are scripts that run before you commit your changes to your VCS.
These hooks can bring functionality commonly found in compilers to languages with very weak or non existent compilers.
In some trivial cases it also is possible to fix errors found by pre-commit tests automatically (e.g. formatting mistakes).
A pre-commit system can be set up via a simple Batch or Bash script, or via tools like pre-commit.