There are a few ways we can tell the difference between animal and human bones. Firstly we have a good look at them, and compare them to our knowledge of human/animal bone shape (morphology). Here we are looking for the right lumps and bumps on the bone in the right places, and the general proportions of the bone. Big animals such as cow, sheep, horse have much thicker, denser bone than humans. If you tap them, they sounds much more ceramic than human bone. We can also look at slivers of bone under the microscope. Big animal bone is built differently in the body, so has a different structure. Animals like sheep, cows, donkeys, giraffes etc have to get up as soon as they are born to avoid predators. This means their bone has to be laid down very fast and has to be very tough. Under the microscope, it has a sort of brick like structure, where the cells are laid overlapping on top of each other like bricks in a brick wall. This makes it very strong. Human bone, on the other hand, has longer to form and build strength, as when we are babies, we don’t have to walk immediately. Our bone cells are laid down more slowly around the blood vessels, and have a sort of concentric ring look to them, like the rings ina tree trunk.
To answer the second part of your question, yes, there are bones that can easily be mistaken for human: pig ribs look just like human ribs (look at this the next time you have bbq pork ribs), and chicken drumstick bones can easily be misidentified as human finger bones. In Canada and the USA, bear paws are often found, and can be misidentified as human hands.