Maybe I missed it in the other responses, or maybe I'm just too blind from a major lack of sleep the last couple weeks, so just in case it wasn't mentioned I'll address a few things here.
You can't distinguish back movements as either thickness or width. If an exercise makes your lats bigger, you'll appear wider. If an exercise makes your upper/middle back bigger it'll make you look thicker. Take a pull-up for example, medium overhand grip. You'll be engaging the lats quite a lot however also you'll engage your upper back, dare I say, about as much. This will build both width and thickness to your back.
I could give more examples but I'll leave it there for now. Otherwise this post will blow out to 3000 words.
Next on the agenda is the carry over from one exercise to another. If you progress on barbell rows, that will carry over to your pull-up strength (any variation). To some extent. However you still need to train the unfamiliar movement in order to become strong in it. The carryover you can witness first hand by how quickly the body adapts to the movement pattern. Complete pull-up newbs might not be able to do more than 2 pull-ups initially. If they have trained rows enough and made progress, you can expect a significant strength increase over a number of weeks as they adapt to the new movement pattern.
How significant? Depends individually. It isn't unheard of increasing the number of reps by 400% over a month.