This is a bit hard to explain by definition, but there is certainly a significant difference in usage.
At the start of a sentence, 「それに、」 is used generally like "also, " and "besides, " would. Starting a sentence with 「他に、」 would be appropriate in more specific circumstances, like "other than those, (there is) also (...)".
Within a sentence, それに would be used as in
I.e. "There is no proof he/she was involved in that". On the other hand, in the middle of a sentence, 他に would indeed used as "besides (x)", as pointed out in a comment. E.g.
"Was there someone else there, besides us?"
would mean something like "Was there someone in 'that thing of ours'?", and even then it would be grammatically suspect.