In the RAM model, you're allowed to do unbounded indirect access (pointers can be arbitrarily large and still fit in a single machine word).
In the Bit Complexity model (no wiki article, sorry), machine words are constant sized. So storing the address of an entry in a table of size $N$ would require $O(lg(N))$ words.
This raises the question: Are you even allowed to do a multi-word random access into a table of size $N$ when using the bit complexity model? It's a bit of a strange operation, because the machine can't "hold the jump in its head" while making it. On the other hand, it could be allowed but cost $O(lg(n))$ time instead of the RAM model's $O(1)$ time.
I realize that this is basically just a definition, with interesting things on either side, but I'm wondering what the common definition is. Is bit complexity just another way of saying "multi-tape turing machine"?