Hit starter button, wait for N1 8%(for instance) it sits at 4%, you never introduce fuel, hence no engine issues,.now your just motoring a starter. Hit starter disengage...
That's a hung start.
That's not a hung start. That's either a weak battery or a starter problem.
A hung start occurs typically when the engine has experienced a lightoff. What you're describing is a failure to lightoff.
If you're motoring the engnine at such a low speed, starter longevity or life just isn't an issue. You're simply looking at a start attempt. If it fails to motor to a minimum speed, then yes, you're shutting down the starter (or closing the start valve, as the case may be) simply because the something isn't allowing it to come up to speed. You may have a bad relay, you may have an internal engine problem, you may have a weak battery (nearly always the case). The start isn't hung, it just never got started.
A hung start will typically begin a normal or possibly slow acceleration, but begin to slow and then stop at some point...often around 30-50%. It may simply stall at that point, or it may slow with an increasing engine temperature. A hung start may go hot, or it may not. A hot start may or may not hang. Often the procedure for a hung or hot start is the same such that they're listed on the checklist as Hot/Hung Start. It could go either way, but neither one is good for the engine, either one could destroy the engine if left unchecked.
What specific aircraft is it to which you are refererring?