Are a bonsai tree and its normal version the same species?
Yes. For any species that it is possible to grow as a bonsai tree, it is also possible to grow that species as a non-bonsai tree. The process of creating a bonsai tree involves growing a tree in a severely restricted pot with a minimal amount of soil, and trimming both the roots and branches to maintain a desired shape and size. It is the small growing space and regular pruning which keeps bonsai trees small, not the genetics of the tree.

You may wish to check the list of species used in bonsai on Wikipedia to get a sense of which species make good bonsai plants.