Difference between HDD (Hard Drive Disk) and SSD (Solid State Drive)?

I recently got a laptop for christmas. While looking over the options I noticed I had the choice of a HDD or SSD. I have a few questions. 1. Why is it that SSD seem to not be able to have the same capacity of HDD? I see HDD that can hold 2TB, while I see SSD that can usually only store 500-750GB. 2. Is there a difference in how the memory is stored on the drive? For instance: Is file "X" going to take up less space on a SSD because of the way it is stored? I understand that RAM takes segments of your HDD and breaks it down to send it to the processor (I know it's more complex than that, but for the sake of time). Since a SSD is flash memory, is it faster at doing this?

TL;DR: Pros and Cons of HDD and SDD. Is there a difference in the way data is saved? Why do most SSD have less capacity than HDD?