An excert from here:

Slacks implies pants of certain materials which are not part of a suit (jeans are not slacks, and you would not refer to the pair of trousers that came with a suit as "slacks".) It is also more common to use "slacks" to refer to pants worn by women, while men would wear "trousers". Meanwhile, "pants" could refer to slacks, or trousers, or jeans, or just about any form of two-legged outer garment for the lower body.

Note that in AE, "pants" by itself is never understood to mean underwear of any kind, and must be altered in some form (either as "underpants" or as "panties") to have that meaning.

Bill: What's this I hear that the boss walked into your office while you were changing your clothes and caught you in your underwear? Tom: No, but she nearly caught me in my underwear; luckily, I had just put my pants on.

This is an AE perspective but, I would say that trousers and pants are synonyms. With both being any outer garment that covers both legs separately and goes from waist to ankles. Technically slacks is also a synonym, but the informal definition I most frequently hear is that slacks = dress pants. I.E. Pants that you might wear if you were trying to look nice.