When you take a picture with the camera app, the picture is stored wherever you told the camera app to store it to (change it by going to the gear icon on the camera, and changing storage location to external SD)
When you use the dropbox app, it doesn't actually save the data to your device. Every time you open the program, it downloads a list of what you have on there. It only downloads when you tell it to save a file (you can press the star icon to have it always keep that file on your device so you aren't limited to where you have a data connection)
If you want to download a file manually from dropbox, find the file you want, and long press it. Select export, and right at the top of the menu that pops up is "save to SD card."
So basically, Dropbox is smart enough to know you probably don't want to bloat your device downloading everything to it, but you can always download stuff at your own leisure.