There is no difference botanically speaking. Pelargonium is the correct name for the genus which has now produce thousands of named cultivars and hybrids and is popularly, though incorrectly, known as 'Geraniums'. Zonal geraniums are just Pelargoniums with dark leaf markings. The garden centre is just confusing things with made up names.

So the flowers are the same size on both?

It's not possible to say that because there are so many different cultivars. The garden centre's terminology is meaningless so one can't draw any conclusions. Here's an old FAQ from the Geranium Forum. Geraniums and Pelargoniums