Let me see if I can expand on what Stewie said.
This is still at a pretty high level, but gives some more detail.
TSH is the request from the pituitary gland to the thyroid to make more thyroid hormone, so if you are in range there, then it means your body thinks you are good, if it is high, it could mean that your thyroid isn't producing enough hormone.
T4 is what is converted into the active hormone, T3, as well as other hormones such as RT3.
If T4 is in range, your thyroid is producing enough hormone, if it is below range it is not.
You can have both TSH and T4 in range and still have hypo symptoms. The next one to check is free T3. This is the active hormone, but again, it can be in range and you can still have hypo symptoms.
The best indicator is the free T3 / RT3 ratio. Essentially RT3 binds to T3 to cancel it out. If your RT3 is high, or the ratio is not right, all your other numbers can be fine, and you will have hypo symptoms.
There are also things like making sure your adrenal system is in check. If your cortisol levels aren't right, all of your hormones levels can be fine, but your body will not respond correctly.
The body is a complex system, sometimes we try to over simplify things too much, which works most of the time, but there are outlier cases.