To take the second question first, any Linux application will run in any distribution. But there are several different packaging systems (like msi files in Windows) in use: rpm, deb, etc. Also, Linux software is integrated. If 2 windows programs use the same dll file, they will each have their own copy, but no matter how many Linux applications you have using a library, they'll all share the same copy. That means that a package has to specify its dependencies and the installer has to check they're installed. That can lead to problems even if 2 distros use the same packaging: Fedora and PCLinuxOS both use rpm, but library A may be in package X in Fedora and package Y in PCLinuxOS. That's why we say "get your software from your own distro unless you know enough to sort out any problems." Luckily, most major distros have a huge range of software:
http://pkgs.org/
http://linuxappfinder.com/alternatives
Now characteristics.
1. Unlike Windows, you can choose your GUI. Most distros offer several, but it's a good idea to use the one they offer as a default, since that gets the most users and is least likely to have bugs. You can choose
Unity: makes your computer look like a smart phone: Ubuntu only
KDE: lots of eye-candy, very configurable: PCLinuxOS, Mepis, Korora
Gnome: quite fancy but less demanding on the hardware than KDE, a bit more tablet-looking: Korora, Parsix
Mate: more traditional in appearance and performance: Mint
Xfce: ditto: Manjaro, SalineOS, ZevenOS
2. Distros vary according to how long they test new programs and so how breakable they are, from bleeding-edge to enterprise quality.
Bleeding edge: Manjaro, Korora (much less so)
Ultra-stable: Mepis, SalineOS
3. The frequency of release also varies. Rolling-release distros change constantly, so you install once and update once a month.
Rolling-release: Manjaro, Mint (Debian edition) PCLinuxOS
6-monthly: Korora, Mint
annual: Mepis, Parsix, SalineOS, ZevenOS
alternate years: Mint {long-term support version)
The ones I've mentioned are just those I think are good-quality, easy to install, and well-off for software.