You can tell what they are from the size of the poo. A cat or a trap dont use poison as they will die somewhere and leave a horrible smell and you may never find where it is. They can get in through small holes, if you can put a pencil in it they can fit through it. Will be the cold weather driving them in, im in the process of stipping out all the old loft insulation and there are hundreds of little mice nests in it and tonnes of poo too (not found any mice yet though)
The rat mess is up to about half an inch in length , mouse droppings are more prolific and about the size of rice grains.
Rats will take and store the food , thats why there are no wrappers, mice will too , but size is more of a problem for them.
Me being a soft git I think poison is barbaric. I have used the sonic devices and they have worked. It is very difficult to keep them out, as has been said secure storage of food helps, like biscuit tins and bread bins.
The poor little bu**-rs are just cold and hungry, hard life innit.