Calibre recognizes the PB360 by name on the PC, too.
That, however, is a matter of communication; of identifying and keeping track of the PB360 folder structure (other readers don't have one) to track the location of onboard content at sync time. (And stuff like that; plumbing.) Its what, among other things, lets Calibre drop its news feeds and recipe-collected "ebooks" into the proper folders, even creating them as needed.
In addition to that identification, which is automatic for a lot of reader models, Calibre also lets you use a target platform, by name, when converting ebooks between formats. That is so it can set up the various defaults that some formats require, so as to produce a useful display. Depending on your input/output formats (say, hard-formatted txt or pdf) it could have an impact on things like margins, font-sizes, zoom levels... Stuff proper reformattable ebooks (lits, prcs, fb2s, most epubs) don't require you to worry about.
As long as your ebooks are in a reformattable ebook format, and DRM-free, FBReader overrides any hard-coding with your own preferences so the ebooks look the way you want them so the choice of target platform rarely if ever matters. And even then, most of the targets are 600x800 resolution 5-6 devices so it really doesn't matter much.
For most people, using Calibre with PB360 is purely transparent; you worry about the ebooks, Calibre and PB360 take care about the plumbing.
Two very good products that together move us a bit closer to ebook nirvana, no?