is installing packages same in all the linux distribution or will this change distribution to distribution

is installing package same in all the linux distribution

Dunno why you posted this twice but in case you forget something or want to rephrase your post you can use the edit button.

Now to your question:
The way distributions install packages various on the programm itself that is used to install. Thereis apt and yum (debian, redhat, centos) Thereis slack-pkg for the slackware users. And many more i don't know of. But they all do the same. Take some files out of a compressed archive and put them into the filesystem. Most of the times there are also some scripts that are run before and/or after the installation. LIke adding a user or configuring certain stuff.

You should check on one choosen distribution and see that you get along with the package manager. If you have question regarding certain distribution I'll help you out.

No. Installing packages in each Linux distribution is entirely different. The way you doing it in fedora may not be the same in Ubuntu.

As zhjim said, most mainstream distros will use package managers such as apt, yum etc. If you start to delve into the more "advanced" (for want of a better word) distros then package management becomes a different beast. Distros such as Arch and Gentoo build packages from source and install, and at the bleeding edge there's the likes of Linux From Scratch, which has no package management whatsoever. It's up to you to find the sources and rebuild packages when you want to update them.

If you are considering a distro and want more specific guidance then you will need to ask for distro specific advice for more information.