I am having a few questions on welds, Say if I take a free model, like a first-person shooter gun as an example. Why are the welds shown here different from local-side to server-side?
Server Sided:
Local Sided:
This confused me if you have any questions or clarifications needed, ask away!
Summary:
Why aren’t the welds happening both server-sided, and local-sided? 
If you created the weld on the local side, then it won’t replicate – even if you parented the gun to the character.
You’d need to weld the gun on the server side to handle all that.
Parts that aren’t descendants of startercharacter that are in the character won’t replicate, I believe.
Server side is what happens universally. What happens on the server side replicates to all clients. However, on the local side, whatever happens there ONLY shows to the CLIENT and will appear normally for everyone else depending on what the server side is showing.
As such, the weld here isn’t done on the server side; the weld has only been applied to the client. To fix this, I would advise using a RemoteEvent and having a script that listens to it to create a weld. Once this is done, have the local script in the tool fire the event for it to function, more specifically on the Tool.Equipped RBXScriptSignal (using Tool.Equipped:Connect(function() or Tool.Equipped:Connect(insert function name if one is present prior) ).
This reply should fix your problems.
The free model I took as I looked closely, was a big mess. The example I took had broken (Server Sided Only.) The answers in this post are not wrong but the free model concluded with messed up values, server-sided (For some reason?). I will next time check out scripts problem’s (where the source is) before asking a question next time.
Fixing the names and debugging it server-sided fixed the problem for me. Thanks to all who helped! 