Yes, there are official records of people affiliated to each party. Those tend to be the ones who support the group economically. If you have a big number of affiliates you have more chances to be stronger in the next elections.
Whenever you sign your affiliation in a political party this information goes to the minister of treasury to control if their fees are transparent.

A brief example of affiliates in my country:
With the exception of Unidas Podemos that you don't need to pay fees to join them

No I mean registered to vote as one party member or another?

In the US there are public records of registered voters, voters by parties, voters by voting--that they voted--not who they voted for--and so forth. There are also records of donations to parties / candidates.

Of course, there are ways of donating $10,000,000 to Candidate Crook without being listed. How is on a need-to-know basis. If you have to ask how, then you don't need to know. Similary, if you need to ask how much it costs to buy a candidate, then you can't afford it.

If there is a "closed primary", voters have to declare which party primary they are voting in. One can become a member of a party. That puts you on a list.

I only ask because I read a poll claiming a certain percent of people of one party affiliation have particular beliefs and I wanted to get a sense of how many people that actually is.

Where can these numbers be found? Is there a government site?