American English:

In American English, "pants" is a general term used to describe any type of clothing worn from the waist to the ankles. This includes what are known as trousers in British English, as well as jeans, slacks, khakis, etc. In American English, "trousers" generally refers to a specific type of pants, often more formal than casual wear. They are typically worn in professional or dressier settings and are similar to what might be called "dress pants."
 
British English:

In British English, "pants" refers to underwear or undergarments for men or women, which is equivalent to what Americans would call "underpants" or "panties." In British English, "trousers" is the standard term used to describe what Americans call "pants." It encompasses all types of pants, including both casual and formal styles. 

"Pull (it) up" is a common phrase used when talking about adjusting clothes, especially when something is slipping down. For example, if your jeans are too loose and start sliding down, you might say, "I need to pull up my jeans." It's also used for things like socks, sleeves, or even a strapless dress. Imagine you're helping a friend get ready, and their dress keeps slipping—you might say, "Hey, your dress is falling down. Pull it up a little!" It's just a simple way to tell someone to lift their clothing back into place.