Welcome to the wonderful wacky world of TERRIERS! Frankly, Terriermon doesn't really look like a terrier at all despite his name. It just makes me think that the designers first drew up a cute little cartoon dog monster, then flipped through a list of dog types and settled on 'terrier' because it would sound cooler than say, Spanielmon.
There are lots of different types of terriers, but let's just speak generally here (this IS a Digimon site after all! If you want dog breed information, go to a dog breed site). Let's see if Terriermon actually DOES have anything in common with his namesakes!
1. Your classic image of a terrier is that of a square, horsey-faced, wire-haired dog with beards and eyebrows to spare. Not Terriermon.
2. Terriers are mostly small and easy to carry around. Terriermon!
3. Terriers love to dig and dirty themselves up. Terriermon!
4. Terriers don't shed naturally, so they need their hair plucked or shaved regularly. Because of this, their skin is prone to irritation. Not Terriermon... I think.
5. Since terriers are very straight-forward and try to cheer their human companions up when they're being all gloomy, terriers would most definitely be really blunt if they could talk. Terriermon!
6. They're insanely protective and don't take too kindly to strangers. Terriermon and not Terriermon. There's no doubt he wants to protect his chums, but he can tell who he can trust and not.
7. Terriers are little balls of energy who don't sleep. Ever. Terriermon and not Terriermon! He sure is a handful, but he loves to chill and relax.
8. Terriers generally have small ears. So very not Terriermon.
In conclusion, I don't feel any more educated than I was before I made this list. I guess only the creators know whether or not they had terriers in mind while developing Terriermon's personality...!
Because I NEVER miss a chance to bring up my dog, here's Fidel, my Airedale Terrier! If he were a Digimon, his name would be AiredaleTerriermon, and he'd have a big horn on his forehead.