Please consider the following graph:
Is there a formal definition for the longest nonrepeating sequence of vertices which form a loop in a graph? (A, G, B, C, D, E, F)
And how about the longest loop without shortcuts? (A, B, C, D)
The closest I'm aware of is the Graph Diameter, but that's obviously very different.
What you call "loop" is more commonly known as a cycle, and there doesn't seem to be any common term other than "longest cycle".
Your "loop without shortcuts" appears to be a chordless cycle. Again, I don't think there's a commonly used nicer term than "longest chordless cycle".