Hi Lisa,
Have you looked at the health page on the subject, it might help to understand it a little.
http://www.medhelp.org/health_pages/Multiple-Sclerosis/Weak-vs-Feeling-Weak/show/1146?cid=36
I can tell the difference between fatigue and weakness, for me fatigue includes cognitive fogginess too but i can feel weak and still mentally feel fine, my usual self, which is very different to fatigue. I do catagorise them seperately but know there is an overlap affect, because i experience different levels of fatigue, i tend to think of fatigue as absolutely dominating. Ignoring the weakness and trying to push through it does lead to temorary fatigue thats lifts with resting, the other type of fatigue doesn't.
If I use your example of being at the mall, by the time I get from the car to the entrance i would be feeling the weakness in my left leg, it feels heavy and starts to not lift very high. I start to veer to the left, oddly wobbling over to the left like someone has suddenly pushed me and my right leg starts to lift higher than it needs too. I think my right leg does this to push out the steps, over compensating for the lack of cooperation coming from my left.
It is all physically and mentally exhausting because you have to overly keep your focus on maintaining balance and walking, which leads to additional fatigue so your not only feeling weak your gaining temporary fatigue. Years before MS was on the radar, i would tell my dr that the ground was calling me, i have to stop no matter what, i just have to lay down or fall down lol this was before i started walking like a (drunk) string puppet.
Listen to what your body is telling you, stop and rest to see if you feel stronger but if it doesn't help, its always time to go home.
Cheers.............JJ