These answers certainly call for a bit more depth. The better you understand pointers, the less bad code you will write.
An array and a pointer are not the same, EXCEPT when they are. Off the top of my head:
int a[2][2] = { 1, 2, 3, 4 };
int (* p)[2] = a;
ASSERT (p[1][1] == a[1][1]);
Array "a" functions exactly the same way as pointer "p." And the compiler knows just as much from each, specifically an address, and how to calculate indexed addresses. But note that array a can't take on new values at run time, whereas p can. So the "pointer" aspect of a is gone by the time the program runs, and only the array is left. Conversely, p itself is only a pointer, it can point to anything or nothing at run time.
Note that the syntax for the pointer declaration is complicated. (That is why I came to stackoverflow in the first place today.) But the need is simple. You need to tell the compiler how to calculate addresses for elements past the first column. (I'm using "column" for the rightmost index.) In this case, we might assume it needs to increment the address ((2*1) + 1) to index [1][1].
However, there are a couple of more things the compiler knows (hopefully), that you might not.
The compiler knows two things: 1) whether the elements are stored sequentially in memory, and 2) whether there really are additional arrays of pointers, or just one pointer/address to the start of the array.
In general, a compile time array is stored sequentially, regardless of dimension(s), with no extra pointers. But to be sure, check the compiler documentation. Thus if the compiler allows you to index a[0][2] it is actually a[1][0], etc. A run time array is however you make it. You can make one dimensional arrays of whatever length you choose, and put their addresses into other arrays, also of whatever length you choose.
And, of course, one reason to muck with any of these is because you are choosing from using run time multiplies, or shifts, or pointer dereferences to index the array. If pointer dereferences are the cheapest, you might need to make arrays of pointers so there is no need to do arithmetic to calculate row addresses. One downside is it requires memory to store the addtional pointers. And note that if the column length is a power of two, the address can be calculated with a shift instead of a multiply. So this might be a good reason to pad the length up--and the compiler could, at least theoretically, do this without telling you! And it might depend on whether you select optimization for speed or space.
Any architecture that is described as "modern" and "powerful" probably does multiplies as fast as dereferences, and these issues go away completely--except for whether your code is correct.