This isn't the only difference you can find between the two species of rodents. Rats tend to have smaller ears in relation to the rest of their larger bodies. They also tend to have a more rounded facial structure as compared to mice which tend to have more pointy features. Also if you have the opportunity to examine the mouse or rat in close proximity, you can count the number of nipples it has. Both male and female mice have five pairs of nipples, and both female and male rats have six pairs of nipples. Something tells me that you're not going to be counting the number of nipples on the rodent. What you really want to know is if you can determine whether you have a rat or mice problem when you haven't even seen the rodent.
One of the common questions is whether you can identify whether you have a mouse vs. rat based on their feces, or poop. The answer is yes, there are ways to tell the difference between mouse and rat feces. The Norway rat, the most common rat you're likely to deal with, has lumpy feces that measures 1/2 inch to 3/4 inch in length, and generally 1/4 inch thick. The ends tend to be rounded or more blunt. The common house mouse on the other hand has smaller excrement that measures 3/16 to 1/2 inch in length and are generally pointed at each end. You can determine whether the feces are fresh or old by the consistency. Fresh trappings tend to be moist or soft, sometimes shiny and dark, but after a while they tend to become dry and hard. Old rodent droppings will crumble, where as newer droppings will not.
If you do find that you have a rat invading your home or your garage, the best defense is a good offense, so I would recommend purchasing routing traps that are specifically designed for rats. Most experienced professional rat exterminators preferred the use of a wooden snap trap to catch rats. Techniques for deploying these traps are similar to catching mice. You'll want to place them along the runways that the rats are using between their nest, or burrows, and their food source. If you'd rather not kill the rats as you capture them, there are some live catch rat traps.
If it's a house mouse that you're up against, I recommend checking out some of the tips and tricks to get rid of mice that are available on this website. Whether you're looking to exterminate mice, humanely catch and release them, or prevent mice from coming into your home in the first place, there are techniques presented on this website that will make your life easier. One more interesting tidbit that may help you in your mice hiding adventures... It is a little publicized fact that rats are known to eat mice, so if you have a mouse problem you may want to deal with it by finding some rats and inviting them over for dinner. How's that as food for thought?
Best of luck in your rat and mouse hunting adventures!