What are the kinds of thyroid hormones they check?

Thyroid. It depends who "they" are. Most primary care doctors only check thyroid function - t4, freet4, tsh. Endocrinologists would also likely check antibodies against thyroid -- tpo, thyroglobulin antibody, TSH receptor antibody or tsi.
TSH. Thyroid stimulating hormone, it is low when there is too much thyroxine; and high when not enough! T-3 is the active form, and t-4 is a pro-/to less active form produced by the thyroid to modulate metabolism.

Related Questions

40 F generally healthy. Recently checked hormones due to hair loss. Thyroid/hormones normal, but testosterone 14 on scale of 20-70. Any relation?

Unlikely. There are a lot of causes of hair loss in females. The pattern needs to be looked at and need to start simple first. One of the most common causes is iron def (w or w/o anemia), recent illness, physical stress. Before getting to worried basic things should be checked. Testosterone in a female also has a lot of controversy. START SIMPLE with a good dermatologist, Gyn or endocrinologist!