Realistically, there's no difference, IMO. People who say Primal are just into Mark Sisson's books, website, etc. Primal is a variant of Paleo. Everyone who eats Paleo eats a different variant of it.
I wrote a post, including a downloadable PDF table, comparing different diets (Primal, Paleo, Gluten-Free, GAPS, Weston A. Price). Check it out!
Welcome! There are so many versions of "Paleo" out there its really hard to keep up. A lot of the differences have to do with acceptance of dairy but also some "safe" starches. I'm pretty new to this way of eating myself. At first its a bit daunting with everyone telling you their version of the "right" way to do Paleo. But just keep in mind that everyone's body is different. Do your research, and find out what is best for you. There is no one "right" way!
There are a great deal of paleo/primal/caveman bloggers and gurus, each with their own gloss on what the perfect diet consists of. Still, none of them are you, and their prescription cannot overrule your self-awareness and knowledge of what works for you. This chart is actually a pretty good description of "strict" paleo. For me, however, paleo is more of a basic set of principles that allow me to eat and live healthy without counting calories or micromanaging my diet.
As far as the paleo/primal difference, primal is Mark Sisson's take on paleo -- he wrote The Primal Blueprint (a great book in my opinion) and maintains a blog. Basically, it's like regular paleo, along with exercise and lifestyle philosophy, and allowance for some "sensible indulges" like dairy, dark chocolate, and wine. Like most books, he presents a general suggestion with enough room to tailor it to fit your life.