What Is the Difference between Signs and Houses?

Theoretically, the difference between signs and houses is easy. If you've been studying astrology at all, I'm sure you've heard that the planets are the what; the signs are the how, and the houses are the where. But when I go to try to interpret a birth chart, I get caught up in interpreting the signs and houses in the same way, like interpreting Moon in the 4th House as the same as Moon in Cancer. They may share some similarities, and you might get some insight by looking at it that way, but it is not quite accurate to interpret that way.

It wasn't until this weekend that I had an epiphany by observing my very Sagittarius friend. I have two 9th House planets (Sun and Mars in Cancer); she has none in the 9th House (Sagittarius's house). I have only outer planets (Jupiter, Uranus, Neptune) in Sagittarius, while she has all those planets plus the Sun in Sagittarius. So, since she has a personal planet there, and I don't, I came to realize that she acts like a Sagittarius, and I don't. I act much more like the Libra/Virgo/Cancer/Leo/Scorpio mix that I am. However, I'm extremely interested in and put lots of energy into 9th House/Sagittarius-like things. I constantly read and study 9th House topics, especially metaphysics, religion, belief systems, ethics, philosophy, astrology (obviously), cosmology, and not so much the mundane and mainstream science stuff of the 3rd House. I want to be a lifelong student. I would go to college the rest of my life if I could make a career out of it. I follow an ethical belief system that I've arrived at on my own. I put a lot of energy into truth seeking and teaching most people in my life. So, even though I don't embody Sagittarius traits - happy-go-lucky, jovial, extroverted, blunt with speech - I am deeply connected to all the things that Jupiter represents. On the other hand, my friend has no planets in the 9th House and invests almost no time and energy into 9th House things. She seems (acts) interested in them, as a Sagittarius, but she does not put her energy into them. She has a stellium in both the 3rd and 5th Houses, so most of her energy goes into talking to friends, information collecting, having fun, performing and creating, being entertained, laughing, and partying. I have no planets in these houses and spend almost no energy on these things.

Another example from my own chart is that I have 2 planets in Cancer and no planets in the 4th House. So, I act like a Cancer - moody, food-loving, animal-loving, sensitive, introverted, quiet (for the most part) - but I don't invest a ton of energy into 4th House things - cleaning/decorating my home, mothering (I strongly dislike most kids and have always hated the idea of being a mother. I do feel extremely maternal to the animals I've had in my life, but I don't even want another animal for a long time because I'm just not so focused on developing a family and home base. I've even gotten tired of cooking.)

Also, I have 4 planets in the 2nd House, but I do not feel like I act like Taurus at all. I am very focused on Taurus things though. I love accumulating money and possessions (mostly just books, which corresponds with my 9th House planets!). I have several collections of small items. I love eating. I love singing. I love stimulating all 5 senses. I am pretty attached to my childhood. I need a lot of physical contact and am very focused on material security (and emotional with all the water in my chart).

I hope that makes sense. Let me know if you have any other insight!