Does tethering and hot spots work the same to get internet on my laptop from my cell phone?

I know I can pay for hot spot, which would give me the ability to get wifi reception on my computer using my phone. I don’t want to pay for that service. I understand there are some free programs, so if you know of any good ones I am interested as long as it is legal. I am not trying to get around any laws.

Now, this tethering thing? I don’t know how it works. Does that mean using a cord between the phone and computer I can get internet on the computer? And, I don’t need a special program?

Thanks.