Since Linux Mint is Ubuntu based, does this means that most of the softwares and commands for software installation & updation will be same?
sudo apt-get install vlc ?
For eg. Will Synaptic Package Manager be common to both ?
Linux Mint is indeed based on Ubuntu, with a number of additional packages, either provided directly by the Mint developers, or patched from Ubuntu packages, or imported from other repositories. This means that any package available in the corresponding release of Ubuntu will also be available in Linux Mint, and the same package management commands can be used.
If you’re using Mint though I recommend you learn its specifics, and use it in the way its developers intended, rather than blindly using techniques cribbed from other distributions. Start by reading the Mint documentation for your release.