That wasn't what I meant. I know your system works differently from say a proportional legislature. What I meant is that what you call a party here is a organization with a program the members (who join and pay their party fees) vote on to determine the goals of the party and a leadership structure elected by the membership base (different from the voting base who are not all members obviously) to try to get elected to then implement their program. Due to that it is also much less person-centric than your system where you elect people for whom parties are a sort of election machine.

So when I hear "party" in my gut the association is with that kind of political organization. The disconnect is not just because of how you slice the political spectrum into fewer sections, but what and how a political party here does things is also different, not merely more defined ideologically.