Hi there,
What you are looking at is the fuel supply, and return lines on your c5, the 97.
The later that you are looking at is the 'returnless' fuel system, with only the supply line to the engine.
You see, in 99, Corvette went to a 'returnless fuel system' to cut down on fuel heating, percolation, and less complexity.
If you look at the diagrams in this and the next post, the top of the photo, shows 2 hose connections on the 97, and only 1 on the 99.
The regulator that has a hose connected to the air intake on your 97 is actually a fuel pressure regulator, and the pipe is a drain in case of leakage.
The 99, that unit is actually a dampener that softens pulses coming from the fuel pump. The pressure regulator, is actually integral inside the fuel filter. That is why the filter on the 99 to present date, is about $50, and the 97-98 filter is only about $22.
So with that, if there are any further questions, please let us know, c4c5