i guess depression is being really really sad sometimes to the point of wanting to die and anxiety is feeling scared or nervous or worrying.

depression has more to do with feeling down, low energy, negative thoughts.

Anxiety is more the opposite end of the scale -- even though the thoughts and feelings are still negative, you can't sleep, can't sit still, feel an imenent sense of doom, heart races, may even have a panic attack, which often feels like a heart attack.

Great answers! I also like WebMD for questions like these:

http://www.webmd.com/anxiety-panic/guide/anxiety-panic-guide-overview-facts

http://www.webmd.com/depression/guide/depression-overview-facts

there 2 totally different illness'.
I agree with starfish; good answer.

I agree with starfish

...is it possible to have both?

Star has hit it right on the nose, and yes, you can have both. They come from two different parts of your brain, or so my psychiatrist says.

depression is more being sad, while anxiety is worrying

it's kinda funny that you're therapist says you can have both. mine told me that i have either one...or the other, but NOT both.

she told me that she's working on figuring out which one i have...

you can have both.

I have both......I am thoroughly depressed, I want to sleep all the time, avoid the phone, feel like crying all the time, take everything anyone says badly, just want ot crawl in a cave. I am also anxious, I worry about everything from the big stuff (hubby's health and the mortgage payment) to the small stuff (are people going to like what I give them, at work I mean) to the normal stuff (driving and such) to the abnormal stuff (I had to pull off the road the other day because I didn't want the gyn to see what I weighed!) Panic attacks and rational and irrational fears are part of my anxiety disorder. It is very confusng and finding the right combo of meds is no fun.

The hardest part for me is the the depression makes me want to sleep all the time but the anxiety won't allow me to sleep. I have these stupid anxious scenarios in my head doing circles around each other.

They can look the same, but they feel different. Unfortunately they can both occur at the same time so it becomes a chicken-or-egg situation.
There's a great passage in the book, "Girl, Interrupted" that uses the metaphor of viscosity (thickness) and velocity (speed).
When I'm depressed, I'm numb, hopeless, and I feel thick. When I'm having an anxiety attack, I'm so inundated with the speed of the thoughts running through my mind that I'm stuck. The depression feeds the anxiety and the anxiety feeds the depression.
My best defense so far for me has been getting enough sleep and drinking enough water.

I have OCD, Anxiety and Dysthymia (a mild/moderate form of depression that lasts years), and they all feed off eachother. It is like a never ending circle. My medication helps control it.