Yes. Depending on which herbie is counting, Thyme Thymus vulgaris has anywhere from 400 to 700 varieties that can cross pollinate. There are upright, creepers and elfin thymes. Some consider the best thymes for culinary use include common thyme, silver thyme and lemon thyme.

A Google search has many hits for thymes.

I've found that most thymes that are advertised without any indication of flavor  English, German, silver, variegated, common, etc.  taste about the same. So I would guess that your English and golden thymes taste very similar. Taste them to find out!

French thyme has narrower, more triangular leaves and a more delicate flavor. It's also less hardy, though I've had it overwinter.

Lemon thyme has a really nice lemony-savory flavor and comes in variations with green or variegated (green with yellow edges) leaves. I generally buy the variegated kind so that I can distinguish it from common thyme in the garden. If your "golden thyme" smells lemony when you rub it, it's variegated lemon thyme.