The first is if the engagement party is being hosted by someone outside your intimate circle and wouldn't know who is invited to the wedding, and the second is if the engagement party will be much larger than the wedding itself.
This second scenario sounds like your situation. If that is the case then there are a couple of things to keep in mind so that nobody gets hurt for not being invited to the wedding.
Make it clear from the outset that the engagement party is the big celebration and event, and that the wedding will be very small, intimate and ceremonial--with very close family only.
Friends understand when an event is family only (and for very close friends), but deciding between which relatives to invite and which to exclude, will cause some hurt.
The short answer is yes, normally you would need to invite all of your family to the wedding, especially if they were all invited to the engagement party.
If it just isn't feasible financially to include all of your relatives at the wedding, or because it's just not what you want, you may have to make your wedding smaller than you anticipated in order to minimize any hurt feelings.
If you clearly define the family guest list by relationship, for example only parents, grandparents, siblings and true uncles and aunts then other family members are more likely to understand why they weren't invited. It's much more difficult to argue with a guest list that's clearly defined and based on relationships.
The issue is if you go half way and choose which relatives to include, then those that weren't invited will inevitably be hurt. And by doing so, you're basically choosing your 'favorites' and letting all your relatives know who your favorite family members are.
Another consideration in all this is who is paying for the wedding. If it's your parents, then they need to be a part of the decision making process. If it's you and your fiance then you have more latitude but still need to consider how traditional your families are and how accepting they might be of the situation.
Although there are longstanding traditions when it comes to engagements and weddings, we firmly believe that you need to do what feels right for you and your future husband, and being respectful and aware of the consequences of your decisions is a big part of that. You obviously already understand that by asking the questions you have.
Congratulations Joyce! We're so excited for the both of you!!!