Then main difference is going to be optimization for readability. In short, the venue in which the font is intended to be displayed (i.e.: designed for) will have characteristics that lend to the functionality of reading it in that venue.
The other difference you might run into is licensing. Make sure your fonts are properly licensed to use in the desired application.
Here's a more in depth article that might steer you in the right direction, that in which I pulled the summary below:
Although they both might be based on the same design, there are usually differences in the design, spacing, and licensing of each. Fonts intended for use on the web are optimized and often modified to enhance readability and performance onscreen in a variety of digital environments. This can include a taller x-height (or reduced ascenders and descenders), wider letterforms, more open counters, heavier thin strokes and serifs, reduced stroke contrast, as well as modified curves and angles for some designs. Another important adjustment – especially for fonts intended for smaller sizes – is more open spacing. All of these factors serve to improve character recognition and overall readability in the non-print environment, which can include the web, ebooks, ereaders, and mobile devices.