As long as your tape width and track width are the same (and in some cases, you can even get around the track width thing; for example, you can play a 16 track 2" tape on a 24 track recorder), after that it comes down to alignment of both machines. Does your recorded tape have alignment tones? If not, can you go back to the original 38 and make some? That would entail recording at least 1K, 10K and 100 Hz reference tones from an oscillator (or from a plugin, such as Audiosuite) at 0 level on the 38's analogue VU meter onto the same type of tape you used before. Then play that tape on the second machine, and you will see exactly what the differences are. In the pro world of machines, one would align the playback machine to be the same as the original. But in the TEAC/Tascam world, it is more difficult to do that. If the differences are major, try to find someone who could align it for you. If minor, just keep them in mind, and work accordingly.
Of course, to back up a step, in a perfect world, you would align the original machine with an MRL, or other alignment tape, before recording in the first place.