When it comes to strength, this kind of strength, functional strength applied with a purpose, I think it comes down to a few things. The biggest, I believe, is using strength correctly so it can be used to the greatest possible effect. In other words, if you think of your mind as the general, and each muscle group as an individual foot-soldier, you have to know which soldier to use, when to use it, how to use it, and which opponent to use it against.
For example, you wouldn't want to put your grip and biceps strength against an opponents hips, legs, or back muscles. Especially not in a straight up one-on-one battle. But in a quick, powerful, unexpected attack it may be possible for your grip/biceps to win a singular battle against those larger muscles groups.
Aside from knowing when to use what muscle groups, I also think individuals have a sort of baseline level of strength that they tend to use when executing whatever movement we're talking about. In the heat of battle, when conscious thought takes a bit of a backseat to instinct and training, some people are hardwired to implement a greater degree of their total strength. These people are also going to feel stronger.
And finally, I believe different individuals possess different kinds of strength. Some possess incredible static strength but not much explosive power. Some are extremely explosive. Some have that ridiculous squeeze. Different people will feel stronger in certain situations.