I read about it all over the place and they say it is a way of preventing pregnancy using contraceptives like condoms, pills, etc. However, in a YouTube video, I heard someone recommending condom use to a guy, saying "Even if your girlfriend is on birth control, I still recommend using a condom." Does this mean that colloquially, US people use birth control to specifically mean contraceptive pills?
Being on birth control means that a girl is taking a contraceptive pill (or injection). Notice the preposition on, which means "regularly taking (a drug or medicine)" (sense 10, here).
Being on birth control is also known as being on the pill (here). Only a female can be on birth control in this sense.
Using birth control refers, more generally, to any contraceptive practice, including condoms, diaphragms, pills, etc. (here). Both males and females can use birth control, in this sense.
Thus, birth control is not used only to refer to female contraceptive pills.