Many apps are only download-able OTA on your phone at mobile sites, so those have to be downloaded OTA. As for Operating Systems (OS), they can be upgraded in one of three ways. The first way is OTA. The second way is OTA through your DM in which DM will download and install the OS directly onto your phone from your computer via USB. The third way would be to download the new OS (since it sounds like one is coming out soon) and install it onto your COMPUTER FIRST. Then you can open DM and it should (should) recognize the new OS. Now you can click upgrade and let DM do the rest of the work. I have been recommended to only use step 3 when upgrading. But, as I said, most apps are download-able OTA only, so in that case there is no difference to be described.
I prefer OTA because you can just email yourself the link and download it through your BB's browser. With DM you need to use BB Desktop manager and it is just a lot easier to use OTA so in my opinion use OTA