Specifically I have an object that is symmetrical in shape, so the UVs are the same and I would like to copy part of the texture to another place of the UV map so that I can put in different details on each of them but use the same starting textures. Here's a screenshot to help clarify what I'm wanting to copy.
Activate the Magic UV addon
After unwrapping the mesh
Select a single face and set the face with the uv texture.
Press U and you get the extra option with UV Magic Addon below
Select Copy/Paste UV -> Copy UV- Default
Then select the face you want to paste or face with similar texture on other side
Select Copy/Paste UV -> Paste UV- Default
First, set your UV Image Editor to 'Paint' and then choose the Clone tool instead of TexDraw. Then set the clone image as the one you are painting so you can use it as a texture to paint with, and move it to position with rmb. Paint at full power to clone the pixels into the new position from the repositioned image. Turn off the clone source and then save the image progress.