Yes, you are right.
There is a theory in astrology that goes something like this; if a certain personality trait is important in a person's life, or if they have some sort of spiritual "lesson" to learn, or test to overcome in order to evolve, than you are going to see that trait indicated in a person's horoscope more than once. Some astrologers say that there is a "rule of three" - if you see indications 3 times, it's a very important life theme.
So, even though we wouldn't see, for example a Moon-Pluto aspect until 1930, we would see, perhaps other planets in a person's 4th house (which rules the home, traditionally associated with the Moon), or in the sign Cancer (ruled by the Moon), or maybe Moon in Scorpio (now assigned rulership by Pluto), or aspects to the Moon or planets in these signs or houses which indicated a similar, but not exactly the same, karmic lesson that the person was working on in this lifetime.
If you are referring to the Sun and Moon, here the term "planet" is not used in its scientific sense, and of course we know this. It is perhaps sloppy for astrologers to go on using the word planet for Sun and Moon, but it's just something which unfortunately has stuck. Sun and Moon are sometimes called the "lights", which is probably less confusing.
...but it basically all boils down to what each astrologer thinks is important. Personally I like to stick to the 10 "planets", Sun through Pluto (by the way, the Sun and Moon are known as planets, even though they are of course, respectively, a star, and a satellite). My reasoning is not very complicated; they are "big and round", and therefore more likely, in my "wooster" opinion, to be important nouns in the language of astrology.
I have always thought that the planets in astrology are more significant than say the asteroids or other bodies, because in kaballah, it says that there are 10 emanations on the Tree Of Life, not 9 and not 11. The spheres on the Tree do seem to correspond symbolically to the known planets (the 7 ancient planets and the 3 outer planets). I suppose that this is what makes my definition (which most astrologers would agree with) real, rather than just picking any orbiting bodies in our solar system.
I hope that I've answered any outstanding questions now, and not generated any more. When I first started to study astrology, I had many questions like this. I know that sKeptics would probably rather be seen dead than in a metaphysical bookstore, but there are many wonderful books on astrology which can answer the more general questions much better than I can.
This might sound strange considering my interest in astrology, but I do actually take a keen interest in science, and I'd like to start a new thread now about diesel fuel, over in the Math and Science section. Hope to see you there.