Yes, size is the best guide. Mouse droppings look like black or dark brown grains of rice. Rat droppings are much larger - about a third to a half inch long and glossy black when fresh.

If you have rats, act quickly before they have a chance to multiply. I had good results with a live trap (Havahart chipmunk trap) baited with oats. The trick is to get them feeding happily on the bait all around the trap before you set it. Then bait and set it. As soon as they use up the scattered bait they will enter the trap since they now regard it as just part of the furniture and the bait as a safe food. I caught six in just over a week and the noises and mess stopped after that.

There are a couple of recent threads about rats and MANY if you go a search of this forum. You'll find all kinds of suggestions. I prefer the live trap because you know where the bodies are (instead of searching for the source of the stench), there is nothing to hurt other critters such as chipmunks and there is no danger or injury or secondary poisoning to family pets. I used a pellet gun at point-blank range to put the trapped rats out of my misery. The blood on the trap is no deterrent to other rats... In fact I think it attracts them.

A word of caution when you start to clean up after these messy guys: wear breathing protection. Mouse and rat droppings carry dangerous pathogens and breating the dust from partially decomposed droppings can make you very ill.