The short answer is that we all have slightly different amounts of different elements, and some animals have very different amounts than we have of some elements. Also, 'we are what we eat', so some animals will eat things with unusual elements in them. Also, we don't even know about all the animal species in the world yet, so we certainly don't know what elements they all have in them. Some more details are below.

My biology book has a nice table about the elements in us - it says there are 92 elements in the earth's crust but only 11 elements are common in us - O, H, Na, Ca, K, Mg, C, P, S, Cl and N. Then it lists the trace elements as: Si, Al, Fe, Mn, F, V, Cr, Cu, B, Co, Zn, Se, Mo, Sn, and I. In words, these elements are oxygen, hydrogen, sodium, calcium, potassium, magnesium, carbon, phosphorous, Sulfur, Chlorine, and Nitrogen; trace elements Silicon, Aluminum, Iron, Manganese, Fluorine, Vanadium, Chromium, Copper, Boron, Cobalt, Zinc, Selenium, Molybdenum, Tin, and Iodine.

There's at least one big difference between us and some simple animals. Our bones, and also sea shells, use lots of calcium (Ca) to help make them stiff and strong. But sponges and some other simple animals that live in the ocean use silicon (Si) to help make their bodies stiff and strong.

Sometimes nutritionists analyze the elements in peoples' hair to learn something about how healthy they are.

I don't know if there are any elements in some animals but not others. When I was in High School in the 1960;s, I learned that our elements are: C HOPKINS CaFe and a few others (we were supposed to remember it as C. Hopkins Cafe), but I know they've discovered V (vanadium) in us since then. And Se (selenium) is in some nutritional supplements now. And we worry if there is too much Hg or Pb in us (mercury or lead). Given how much has been learned about the elements in us since the 1960's, I expect that we don't know for sure exactly what elements are in all the different animals. I'll see what I can find at www.google.com ... not much. But you can look up "periodic table" to find all the elements.