Might the derivation have helped? Interest is a Latin remark, meaning "It makes a difference". At least it has given some pleasure to etymologists. The English borrowed it in the 15th century and, in defiance of grammar, made it into a noun. Such a change of function is not unusual. An exeat, the Latin for "He or she may leave", is another example (as for that matter is a laisser passer). Lawyers, with their non assumpsits and their nolle prosequis, have always enjoyed turning verbs into nouns, and interest was another of theirs, having begun its English career as a legal term, meaning a right or title. The English verb interest, incidentally, as in sentences like "I'd be interested in your opinion" or "Can I interest you in some pudding?" has a different and more confusing etymology, though it comes from the same Latin source.
Anyway, those 10 meanings of the noun divide roughly into two kinds. There are those implying influence or advantage, or a share in something; and there are the gentler ones that suggest enthusiasm, involvement or concern. The first kind has been the commoner. I suppose MPs could argue that what's good for them is good for the country, in which case their interests and ours coincide; but we don't have to believe all of them all the time.