The whole point of the '2nd' part is that it plays other notes in the key of the piece, and usually of the chord which that section of the bar is set in.

Briefly, it can move in the same direction (parallel), opposite direction (counterpoint), at the same pace, or often slower, rarely faster. It can usually be thought of as 'harmonising. There can also be 'incidental' or 'passing' notes to move from one of the 'main' types notes mentioned above.

Now you are thoroughly confused by the theory, aren't you?... :-)