I'm new to blender so I may be mis-explaining this my core problem is that when I add a texture to my mesh the render looks weird and triangulated. I have two meshes that have the same number of vertices,edges, etc (but some edges are different length/scaling). I transfer the UV map of one mesh to the other and then this is the problem that I encounter. In the UV Editing tab of the mesh the UV map looks good, but the texture looks weird (see screenshot) - I noticed that if I try to move a vertex in the UVmap it often won't move all the edges, but seems to be a duplicate vertex with only some edges connected. I have screenshots attached that hopefully explain it better than I am.
The red circle is around one single vertexc in the mesh, but is represented by 5 vertices in the UV map. I assume this is causing my trianglular artifacting I'm seeing.