They definitely look like Gopher holes. I would suggest Castor bean seeds. You have to dig out the hole and place the seeds as deep as you can in the hole. The gopher will eventually come back to bury the hole and hopefully take the bait. I used to put a water hose in the hole and sit and wait with BB gun in hand but that could use quite a bit of water and washes soil out of the holes which leads to cave-ins throughout the yard. After using Castor beans we didn't see gophers for several years.

I've seen lots and lots of mole hills just like that. Do you have lots of the in your yard? Are they within close proximity to each other?

I've even seen shrews build those types of mounds.

Hard to say from the angle. A slightly wider shot would help. It could be moles. It looks like the soil is pushed up. If it is moles, then the gopher killer won't work. It is probably a pellet product, and moles are insectivores, specifically they eat earthworms and grubs. They won't eat the pellets with any regularity. Go back to Home Depot and ask them for a product called Tomcat brand Mole Killer. If they don't have it, I know Lowe's does. It's shaped like a worm, which makes sense, since Moles eat worms. However, I've used it a few times, and it has never failed me. As long as you follow the directions, it should get rid of the mole within a couple of days.