As per my knowledge 3 type of assert method is generally used in System Class in Salesforce.
These are as follows:
assert(condition, msg)
Asserts that the specified condition is true. If it is not, a fatal error is returned that causes code execution to halt.
assertEquals(expected, actual, msg)
Asserts that the first two arguments are the same. If they are not, a fatal error is returned that causes code execution to halt.
assertNotEquals(expected, actual, msg)
Asserts that the first two arguments are different. If they are the same, a fatal error is returned that causes code execution to halt.