Here’s an example of a historical one, this is from U-47 under Prien.
http://www.uboatarchive.net/U-47/KTB47-6Sketch.htm
These were more for situational awareness and were often appended to the KTB (logbook of the patrol) when handed to BdU. In rarer cases they were used for the actual data gathering (in these cases you’ll read in the KTB “Schussunterlagen erkoppelt” - shooting data obtained by plotting).
As mentioned before, Ausdampfen (matching) was more common, BUT that also could involve plotting own boat movements.
Here’s an example:
U-625 (Hans Benker) mentions in the KTB of its first patrol having missed a steamer, and wanting to remeasure its speed:
“Place myself in its wake and match him again using the radar. This works very well and is more accurate than when I only plotted along with him. First of all much quicker. He now runs at 10 knots”.
What’s happening here is he’s using the generated range from his radar to make sure he stays the exact same range behind the target and keeps the target on his bow, then he knows he has matched course and speed. However, certainly not all boats had radar, hence why he mentions the plotting; had he not had radar he would have plotted his own boat’s movement, keeping the target visibly at about the same range in front of him over a certain period of time, and then averaged his speed as the target speed over that measured length of time. Inherently less accurate, which is why he mentions that. This type of plotting was more common, made easier by the fact the boats had a pit log (odometer).
To answer your question about why plots like a maneuvering board plot (in other words a relative motion plot) weren’t used ubiquitously, that I’m not sure about. The unreliable range problem, the lack of surface rangefinding capability is probably a factor, which made the matching of course and speed actually more practical than plotting in many cases. That’s why most commonly in these logbooks you see them either doing this in the target's wake, or overhauling to directly in front of it and doing it in front, traveling along at the target speed and just matching its maneuvers.