These are general terms, there are many more specific terms. For example, briefs, and boxer shorts are two types of underpants in American English. Jeans, corduroys, chinos, and slacks are several types of pants in American English.

The word trousers is also used in American English for many types of pants. Trousers are generally more formal. Pants, the general term, can always used for both formal and informal pants. But cargo pants, parachute pants or bottoms, and sweat pants are always called pants. Jeans can be referred to as trousers, but that may seem a little formal. The word trousers is more appropriate for corduroys, and chinos, still more for slacks, and perhaps most appropriate for the pants that come with a suit.

One definition of trousers says that they have belt loops, a zipper, and are tailored. The term is usually used more broadly than that, but belt loops and a zipper might be good defining characteristics. I believe most men wear pants or trousers off the rack, and not tailored.

When woman wear lose clothing with legs they are usually called pants in America. Dresses and skirts are the traditional formal wear of women. So the term pants suggests that they are less formal or traditional. However, Wikipedia says that the term trousers is sometimes used for women's wear. This may reflect the advance of feminism and perhaps the fact that pants for women were accepted generations ago and are now considered formal.

It is perhaps not surprising that the English use the more formal term more extensively. Americans think of the English as more formal.

The English and the Irish follow English usage. Americans, Canadians, Australians, and even some of the British follow the American usage. In terms of numbers the American usage is probably five to six times more common, but Americans will often not even notice if you use the British forms. The British are probably more picky, but perhaps less likely to be confused as through television and movies they are likely to know American usage.

In many videos concerning the differences between American and British English they say the English use this word and the Americans use that word. As an American I notice that Americans also use the English term, but perhaps a little less frequently. Sometimes as in the case of pants vs. trousers, the words have different shades of meaning in England and America.