EE is for Express Entry.
CRS - means the points you get in that system.
EE is the system where you can get invitation to apply online on a federal level
If you go through province nomination, then you need to get PNP first and then you have to apply on the federal level anyway. There are 2 ways how to apply then - either a paper based application (send by normal mail). Or an online application if your nomination is given under EE. Then you will get invitation to apply next draw.
As you can see people were asking about your EE points. And because you mixed it up with Manitoba points, that is why you got an answer that you should have been invited.
As for Manitoba PNP, please check first if you meet all conditions there (not just the points wise).