One has rust the other doesn't and they both are old.
Tl;dr for TFG
Clean them really good. I use course salt and a clean dry wash rag. If its got a lot of rust you want to empty the salt when it turns gray and rust colored and put in some fresh. Use alot of salt its cheap.
After that rinse it out. The one time its okay to use a little soapy water to make sure you get it really clean. Just make sure you rinse it really good.
Then thoroughly dry it.
Next rub it down with Crisco shortening. Rub down the whole thing inside out, bottom, sides and handle. Use a clean dry wash rag or paper towel. Be careful with a rag until it gets saturated itll leave lent.
After rubbing it down real good use a paper towel to rub off any excess. Rub it down like you're trying to get the shortening off the skillet.
Preheat your oven to 400°.
Then turn the skillet upside-down on a sheet pan and put it on the middle rack in the oven for at least an hour. Turn the oven off and let the skillet cool in the oven.
Repeat that (rub it down with shortening and put it in the oven) as many times as you want, at least 2 or 3.
As soon as I finish using mine while its still really hot, I rinse it under hot water. That cools it down just enough I can scrap it with a plastic spatula if needed without melting it.
Then I dry it with a towel and rub it down with olive oil while its still warm.
Olive oil is the best for several reason but because its low smoke point you can't really use it to season with in the beginning. But after use its perfect.
Don't use too much shortening in the beginning or too much oil after. Always remove as much excess as possible or it will get gummy and sticky. Then you'll have to start all over with cleaning it with salt and seasoning again.
That's how I do it and it works perfectly for me. There are other ways that are easier including using a dishwasher. You'll need to seek advice or instructions on those from someone else.