Can Robot Models for simulations be used in all ROS versions?

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The issue you are running into is not one of whether the simulation works, but whether the simulations have been released as debian (ie: .deb) packages for a specific OS and ROS release.

Seeing as you tagged this melodic, I'm going to assume you are running Ubuntu Bionic.

On a Bionic machine you cannot install packages built for ROS Indigo -- that version of ROS just isn't supported on Ubuntu Bionic (see REP-3).

And since fetch_gazebo_demo (the ROS package) has not been released for Melodic, trying to install it using apt-get will also not work: the debian package simply doesn't exist (see status_page/ros_melodic_default.html?q=fetch_).

Now as to the question of whether simulations (and I'm assuming Gazebo simulations here) created for ROS Indigo will work on ROS Melodic: the question is more subtle than that. ROS Indigo installed Gazebo 2.2 by default (see REP-3 again). ROS Melodic comes with Gazebo 9 (see REP-3).

There are quite a few changes between these two versions of Gazebo (and about 6 major versions), both in terms of the API and ABI as well as the dynamic behaviour of the simulator and the things that are simulated (Gazebo 9 has become a lot more realistic in its simulation than Gazebo 2 ever was).

So even while things (ie: plugins or Gazebo models) may work (ie: load) perhaps after fixing some incompatible things, the behaviour they exhibit in Gazebo 9 vs Gazebo 2 may be so different that we can no longer state that they "work".

Note that I'm not referring to the Fetch packages that you mention -- I don't know whether they work -- but wanted to address your question in general.