Why is birth control called birth control? [Details inside].

Some weeks ago I saw an episode of I Didn’t Know I Was Pregnant in which a girl, who didn’t know she was pregnant, ended up in hospital because she was in terrible pain.
The doctor came back to her room with the results of some kind of test and told her she was in labour, to which the girl responded with the line: “That is impossible, I am on birth control.”
That got me thinking; Why is it called birth control when it is more controlling-/preventing you from conceiving if I am not wrong ?
I mean, it (the pill/condoms/IDU) is obviously not meant to keep you from giving birth after you carried a baby for nine months.
Is it a wrongly chosen name for it, or am I over thinking this?