Huh, interesting. I wouldn't really think of a skillet a pan, but I would call it a frying pan. Some words related to these terms are confusing for me because of the dialects in my area. For example, my family calls peppers "mangos"
This is very different. I am careful with what I say with certainty and what I ask or try to discuss. A tshirt and a shirt aren't necessarily the same, but it is common in American English to say "shirt" for any shirt, including a tshirt. Not all shirts are tshirts, but all tshirts are shirts, so the terms are often used interchangeably unless it is important to be specific.
People are lazy, we don't like to use extra syllables. That is why people usually say TV or fridge.