Not really because of the multitude of higher plant and animal structures: ectoderm, dermis, epidermis, cuticle... and so on.
For the best possible guess - I vote for epidermis. This is just a not very useful wild guess.
PS: angiosperm bark is usually called phelloderm. Two names.
The correct answer is: no. You can make a case for some of them being "most common" in certain contexts, maybe. But in the early days of Biology, researchers categorized everything often uniquely. Read: they went overboard naming things. If something has a name then you think you have a handle on it. When you may have no clue. Example: math graduate students will identify a type of problem and then not be able to solve it. Somehow naming something implies knowledge... not really but we often feel that way. It is called the cubbyhole effect. See, it is self-referential, and it has a name, too! It is a disease. :) ...aaahhhh!
So the outermost layer of plants can be phelloderm, spines, cuticle, trichomes (kind of hair), epidermis, glochids... ad nauseum. Same with animals - fur, spines, scales, exoskeleton.
If you follow the development of tissues in the embryo of plants and animals you can see a common source, but in the full grown organism it is not always evident how a tissue is derived from other tissues.
This requires a lot of painstaking work.
Hair and fur are derived from follicles. Some invertebrates have an exoskeleton so the outer layer doubles as a skeletal structure - crabs, insects, bivalves are examples. Exoskeletons are quite varied.
https://en.wikipedia.org/wiki/Exoskeleton#Evolution.