No, that's not quite right.
You need to choose how best to present yourself so as to fit the requirements, and enable the INZ officials to tick their checklists with the least headaches. Their model assumes that a person has a skilled career - one. People who are multi-skilled, and say so, seem to confuse the system. It's as though the assumption is that working in more than one specialism somehow makes one less good at all of them (although of course that isn't so). I remember someone on here who seriously thought about putting in his EOI with proof of his two parallel careers, but was persuaded against that by a Licensed Immigration Adviser, who pointed out the large amount of extra proof that would be needed, which would have made the processing take m-u-c-h longer than normal.
As far as points for your qualifications and work experience are concerned, you can use the ones that relate to the skill you have put forward on the EOI as your career. Suppose you have a bachelor's degree in that field, which is on the long term skills shortage list.
http://skillshortages.immigration.govt.nz/ And suppose your bachelor's degree is either exempt from assessment, or you get an IQA saying it is comparable to one of the ones mentioned in the LTSSL drop down box on that page. Related just to this one qualification (and of course, you have the right to more points for other matters), you would then get 50 points for your qualification, and the right to add on 10 bonus points for the qualification being in an an area of absolute skills shortage, and 10 or 15 (extra) bonus points for your work experience in that career to date (depending on how many years' experience you have). Suppose you also have, besides that bachelor's degree, a master's or doctorate in a different subject area, you can claim 60 points (instead of the first 50), as those are allowed for your highest level qualification (and you're right to think that points don't accumulate for multiple qualifications under this heading), but meantime the bachelor's still counts for you to have the bonus points relevant to the LTSSL career.