Transparent and pure white are both non-printing.
Transparent means "do not print."
Pure white means "print something here: no amount of cyan, no amount of magenta, no amount of yellow, and no amount of black." That still leaves nothing printed.
In all cases that I can think of, both accomplish the same task.
Except...
If you are printing non-color (varnishes, foils, etc.), you'll often need to have transparency.
Transparent means "do not print."
Pure white (or any color or design) means "print something here" and the color doesn't matter. Varnishes and spot coatings are either on or off. This is masking as opposed to printing.
Your printing establishment knows these things and will prepare to print correctly.
If the background in your file is slightly off-white, whether it's grey or tan or pink, something will attempt to print. Light and/or subtle colors are different than what you'll see when working on the files, as your light colors are printing over stock of some color. No paper stock is perfect white.
EDIT: There are exceptions to these, of course... printing a design with white on a black shirt is an easy example. In your case, I don't think any number of exceptions will apply.