A Tamron lens is my preferred option as I used to have one for my old Minolta when I used 35mm film.

That's all well and good; I'm sure Tamron appreciates your brand loyalty. That being said, there are a plethora of good lenses made by Tamron, Canon, Sigma, etc., and a plethora of absolute garbage lenses. Do your homework on a specific lens - the brand doesn't mean much to inherent quality.

The motor in my EOS 60D is a USM.

No, it's not. Some Nikon cameras have an autofocus motor in the body. All Canon cameras do not. Canon uses a couple of different types of autofocus motor in their lenses. See these existing questions for more info:

What does STM mean on a Canon lens?

What is Nano USM and how does it compare to an STM or USM lens?

I believe I need a USD Tamron lens, but I am unsure. I see HLD Tamron lens on the market that make reference to APS-C format but I am unsure if this is compatible with my EOS 60D.

The USD stands for Ultrasonic Silent Drive. This has nothing to do with the mount. (It's a designation for type of autofocus technology)

The HLD stands for High refraction, low dispersion. This has nothing to do with the mount. (It's a glass technology that affects image quality)

So, why do some brands put all the crap into the product name? Simple: to show off. Instead of offering a simple 15-30mm f/2.8 and putting the specs in the description, they name it the SP 15-30mm f/2.8 Di VC USD G2. Note that this name does not include the actual mount, as it comes in both the Nikon and Canon flavors. (Typically, the mount name will be appended to the name or the lens listed as "For Canon EF" or "For Nikon F")

Unfortunately, there's no way around learning a thing or two about lens technology if you want to be an educated buyer. You'll need to learn about stabilization tech, which Canon calls IS and Tamron calls VC, among all of the other acronyms that will affect the lens.

Advice is welcome.

Your Canon 60D uses the Canon EF mount. This mount has existed since 1987 - there are a lot of lenses for it, and they work with any Canon autofocus camera - film or digital.

Your Canon 60D can also attach to EF-S lenses. I like to think of this as EF-small. This is because the original lens lineup (EF) was designed to work with the size of a 35mm film frame. Your 60D uses a sensor size called APS-C. This is smaller than a 35mm frame. Canon introduced lenses designed for this smaller frame and designated them EF-S.