What is the difference in feeling between working the voice strongly & powerfully (good) & pushing or straining or constricting (bad)?

It depends on which particular muscles are being used to create the power. The vocal folds themselves are a muscle tissue and it is quite desirable that they be worked & strengthened. Initially they may become tired when this happens to them, resulting in a slight quivery feeling, or softness of speech. This does not mean they have been used the wrong way - simply that your vocal stamina has to build up gradually. It is similar to going on a 4 hour bush walk, when you're not used to doing that - there will be fatigue in the muscles, but no lasting damage, as long as you warmed up and down before & after exercise, & took the walk gradually.

Vocal damage occurs when throat muscles that are external to the larynx get involved on the act, & the singer pushes or strains for more volume, or for a high note that is beyond the reach of their current breath support. You will know you are doing things the wrong way if there is constriction in the throat, or tightness when you sing, or you get a sore voice or a husky or itchy throat, like as if you want to cough but don't really need to. These extrinsic throat muscles get involved when there isn't enough air pressure coming through from the lungs. The solution is twofold. 1) Open the throat & 2) Increase the flow of air from the stomach or lower back.

Other ideas for opening the throat are to imagine you are swallowing a tennis ball or a hot potato when you sing, & are trying to open the throat to get it down.