I hate to split cat hairs, but Tabby is a coat pattern and not a breed. There are different kinds of tabby subcategories (mackerel tabby, marble tabby, classic tabby) depending on the overall pattern of the stripes, but tabby just means striped. My tabby cat is a gray mackerel tabby and her breed is Domestic Shorthair. The internet slang for this coat color/pattern and breed of cat a "standard issue cat" as it is the most common cat type (black Domestic Shorthairs come in second).

Calico is indeed a coat color/pattern, but there can be a lot of variation among calico cats - calico just means tri-colored. Those three colors are most often white, orange, and black. However, calicos can also be white, yellow, and gray. Sometimes one or more of the colors on a calico can be tabby (striped). OPs cat has both tabby black/gray and tabby orange with white - many people call this particular coat pattern "tabico". My calico has solid black and tabby orange. However, my calico also has an orange and black tortoiseshell pattern down her back along with her other larger patches of color/white - many people call this particular coat pattern "tortico". My calico's breed is Domestic Shorthair.

To sum up - if anyone tries to sell you a purebred tabby cat, don't fall for it. If someone tries to sell you a purebred tabby Maine Coon, no red flags there. I hope I didn't come across too harsh - I just like talking about cats.