Sympathizer:  Anyone can sympathize with whatever or however many parties they choose.  Though mostly there is little sympathy for any party.

Registered voter:  Anyone who votes.  I believe the laws vary by state, but often you have to choose a party if you want to vote in the primaries.  All this means is you tell them what ballot you want.  You don't have any obligation to whichever party you choose.  Some states don't ask you to declare a party at all.  The problem with this is that it can lead to abuse of the primary system.

Volunteer helper:  Anyone can volunteer for any candidate they choose. They can also go to their local party organization and ask to volunteer, to do precinct work, canvassing, etc.

Donor:  Anyone can give to any party they want, though there are limits on how much you can give.  Or you can sidestep the party and give directly to a candidate.  Again, there are limits on how much you can give them.

Dues-paying card-carrying member:  I am not aware of any "dues."  I do know that if you donate any money at all, you get on a mailing list.  I don't know if you get a card, but I don't think it really means anything if you do.  The card doesn't give you special access to people.  Connections and money do...  

Member of the apparatus of the party:  Depending on your role, you can be elected or appointed.  It varies widely from area to area, and from the local party to the national party, from position to position.  It's really confusing.  I think in most cases you can just start going to meetings, and after you've committed so much time, you can become a voting member, and then you can run for chair of your local party and be elected by fellow voting members.  Technically, anyone can do this.  Then there is the state-wide party.  I don't know if seats in it are elected or appointed.  But they don't really do anything either...   Then there is the national party: RNC, DNC, etc.  You can be hired as a staffer or elected as a voting member.  The DNC members I know are basically go-getter politicians.  Like the dif. between being a diarist and nd admin at ET.  Either way, the main role of the national party is fundraising and nominating a Pres. candidate, which is a formality anyway because this is decided by primary elections.  The main role of the local party is fundraising, precinct organization and sometimes community organizing.  But all of this varies widely from place to place.  The party apparatus is composed of self-organizing entities which are usually devoid of any organization...  Bylaws?  What are bylaws?  sigh....

Then you have every variety of caucus: by region, race, creed, gender, special issues, etc. etc. which can represent a party.  I could set up an organization called "Chicago Democrats to impeach Daley" and it would be perfectly legal.  The party goons here have no respect for the law, so I might end up with bricks tied to my feet at the bottom of the river, but I could legally do it.

So far as party organizations go, outside the national level, it's really the wild wild west.  Which means they can be as corrupt as they want to be and disenfranchise everyone, but you can also start your own organization if you don't like the one you have.  This does happen and sometimes these organizations become very successful.  But the party apparatus really is a fundraising, gate-keeping entity which few regular citizens ever have any interest in or contact with...  

For the average Joe, parties are like sports teams.  You pick one and root for them and hope the other team loses.  

"Pretending that you already know the answer when you don't is not actually very helpful." ~Migeru.