The sign for a trill is 'tr' (in bold italics). The wavy trill line is used to indicate the extent of the trill. The trill line is optional for a single note value, but it's necessary for tied notes.
The wavy line by itself is not enough (sometimes it's misused for other purposes e.g. vibrato).
The wavy line alone means 'trill', so there's no real need to put 'tr' at all. So, it's one or the other. If there's tr and a long wavy line, that means keep on trilling until the end of that line, where there's often a couple of grace notes leading to the next, un-trilled, note.