Shrews are insectivores, so they are looking for bugs, and can be very viscous little critters. They are similar to moles, but they aren't as strange looking.
Rats are quite distinctive, big ears, and they are meaty critters. We get them here yearly in my shed. We use bait boxes with Tom cat poison. Most die in their holes within a week. I've only seen dead ones out in the open twice in a decade. Traps don't work here for rats.
We do trap mice. They are easy with some peanut butter. We see mostly deer mice and house mice here.
Here we also have what we call field mice. They are bigger and more robust, and have a shorter tail. They can sometimes be mistaken for small rat. Those are usually just out in the hay field, and don't come into the buildings.
Generally in the fall here we see an increase in rodents trying to find a nice warm place to winter close to food. We generally only put out poison during a few weeks, than we put everything away.
While it's out I'm always afraid of secondary poisoning as well, but I've never seen it. We place the boxes where nothing can get into them except for the rodents, and we use the blocks so nothing gets dragged off.
This year was a high rodent year. They started early, so we did too. We are still trapping a few mice, but we haven't seen any signs of rats lately thankfully.