Valve train would pertain to anything to do with the valves, such as late or early valve timing, sticking valves, weak valve springs, etc. If you have an adjustable cam sprocket, the vacuum gauge might help show if it's adjusted correctly.
Intake leaks would pertain to the introduction of air anywhere below the throttle plate, as this air has not been taken into account by the carb as it provides the fuel/air mix needed to run the engine. As you posted, loose fasteners could result in an intake air leak, or what people might also call a vacuum leak. All other settings being equal, a vacuum leak is virtually always going to result in a leaner mixture.
A vac gauge is a little "old skool" but can be useful, if only to help rule out possibilities.
All that being said, if your manifold setup does not have an opening onto which you can affix the hose for the vacuum gauge, then unfortunately it's a moot point:whistle: