What is the difference between RAM and TM?
Turing machines are not as efficient as RAM machines. A RAM machine can access an arbitrary tape location in $O(1)$. A Turing machine can't. A RAM machine can do arithmetic in $O(1)$ (under certain restrictions). A Turing machine can't.

Turing machines polynomially simulate RAM machines, that is, for some constant $c$, any RAM machine running in time $O(n^k)$ can be simulated by a Turing machine running in time $O(n^{ck})$. (The constant is pretty reasonable, about $2$, depending on the Turing machine model.)