i am confused that they both mean 'to introduce'.
which word do i use to mean 'to introduce' in this context?
do you have better words or more colloquial words to express 'to introduce'?
In line with what it-ogo has said about the words having several meanings, to get suitable colloquial translation, you have to get the word that has the central meaning you want.

'To introduce' in English having the meaning 'to become acquainted' would be something like познакомиться.