Any way to make a binary in a Linux distribution and run it on another distribution with same architecture? Or I should compile and build it on different distributions?
Is there any compatibility between Redhat, Debian based distributions for binary files? (I want to use my Ubuntu binary file on fedora!)
Normally it's ok to use binaries across linux distributions as long as you have the same set of libraries available. You can use 'ldd' to check which libraries are needed by a binary. libc should sure have the same version in the distributions involved.
Statically linking your binaries makes them LESS portable because some libraries won't then work correctly for that machine (differing authentication methods, etc).
If you statically link any "unusual" libraries and keep your set of supported distros to a minimum, you should be ok.
Don't statically link the C library (or the whole binary), that's a recipe for trouble :)
Look at what (e.g.) Google do with Chrome.
LSB is definitely worth checking out. Though in regards of working with libraries I was most satisfied by this answer here at SO https://stackoverflow.com/questions/1209674/shipping-closed-source-application-for-linux/1242738#1242738 and this detailed treatment of the rpath mechanism http://www.eyrie.org/~eagle/notes/rpath.html