Softpastels are dry crayons, you can compare it with those crayons they use on a schoolbord. 
There are different kind of softeastels: hard softpastels and soft softpastels. I work with both of these. 

I mostly work with soft softpastels. These (most of the time) are circular sticks. They really stick to the paper and is easy to rub out. 

Hard softpastels are (most of the tie) little square shaped sticks. They are great to use for details, since they're so hard. They're a little bit harder to rub out though. 

The hardness from both of the pastels differs with the brands. Schmincke is a lot softer than Rembrandt for example. 

Pastels are made from pigments mixed with Arabic gom. You can layer soft pastels really well, not only darker colours over lighter colours, but also lighter colours over darker colours. 

And then there are pastel pencils. These are the same as the soft softpastels, except they're pencil shaped, meaning you can use these for detailing or (in my case) draw fur. Something great about pastel pencils is that your hands won't get dirty while working with them (if you're working with the crayons they'll get dirty). They're not great for working on big surfaces. 

When saying pastels, you're probably thinking about these soft pastel colours. You can get pastels in every colour you want though. Not only the soft colours, but also the bright colours, the browns, etc. 
Working with pastels is more painting then drawing, therefor, a lot of people who work with pastels rather say they're painters than drawers.