What is the differences between flavour & distribution?

Well, technically Linux is "NOT" a UNIX. It uses the Linux kernel and the GNU userland utilities. As such GNU stands for "Gnu's Not Unix" and instead is a UNIX-like operating environment.

Also, while AIX, Solaris, BSD, HP-UX and even Mac OSX are "UNIX" depending on the actual certification from whoever holds the rights to determine what UNIX is, many people lump them together as the tools are similar and the commands are similar in most cases.

In the case of a distribution, that is due to the maintainer's decisions of what to include, how to control the releases, etc.

SUSE, Debian, Red Hat, are all using the Linux kernel, GNU userland, etc, however Debian uses different package management, for the most part, Different run levels and configuration files are employed, and the choice of what goes into a release is left up to the maintainer of each distribution.
 

Distribution means a certain set of applications that are bundled and pre-configured. The difference in that for Linux distributions (or distros) can range from almost nothing (eg. RHEL vs. CentOS), to a completely different intention, and thus software selection (eg. Slackware vs. Mint)

Different "flavours" are called that because they are based on the same principles (POSIX, Single UNIX Specification), but follow different ways for implementation. For example, while all Unices have a sigaction system call, probably none of them share the same implementation, as the Kernel itself follows different specifications.
 

Which Linux type resembles the tailor-made Syno one?

The Synology OS uses the Linux Kernel only, it does not use any specific flavor/distribution of Linux.
 

Want to do networking on linux, so which linux flavour is prefer for networking.

The best way to choose is to download and burn some live CDs and see what you prefer.

Kanotix and Ubuntu are good distros, and the Kanotix CD has many more included apps than the Ubuntu, though you can apt-get all you like for either.

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