Is there a fifferences between testing a tsh, t3, (liothyronine) and t4? what kind of test is a tsh?

Thyroid tests: The TSH (thyroid simulating hormone) is the most important test of your thyroid function. It's the pituitary/brain signal to your thyroid to make more thyroid hormones t3 (liothyronine) (tri-iodothyronine) and T4 (thyroxine). Elevated TSH means low thyroid function. Unmeasurable/very low TSH means too active thyroid. T3 (liothyronine) is short acting. T4 (thyroxine) is longer lived, usually given for thyroid replacement.