What is the difference between Static & Dynamic Testing?

Questions is quitely in general, since test method is not provided, application to the test method not also mentioned, e.g civil works, mechanical, etc.

Understanding the questions, static testing are test carried out on a certain structures is considered at rest (no motion involved). Best examples for this is the load test for structural component. (no impact load and the dead weight of objects are applied)

Dynamic Test on the other hand, its simple a test procedures engage in motion "Movement". Best example is pile dynamic test, this test applied dynamic movement for which the strucure are tested to measure strength, bearing pressures, skin friction of the piles, many others.