Single-element indexing
For single elements indexing as in your example, the result is indeed the same. Although as stated in the docs:
So note that x[0,2] = x[0][2] though the second case is more
inefficient as a new temporary array is created after the first index
that is subsequently indexed by 2.
emphasis mine
Array indexing
In this case, not only that double-indexing is less efficient - it simply gives different results. Let's look at an example:
>>> arr = np.array([[1, 2], [3, 4], [5, 6]])
>>> arr[1:][0]
[3 4]
>>> arr[1:, 0]
[3 5]
In the first case, we create a new array after the first index which is all rows from index 1 onwards:
>>> arr[1:]
[[3 4]
[5 6]]
Then we simply take the first element of that new array which is [3 4].
In the second case, we use numpy indexing which doesn't index the elements but indexes the dimensions. So instead of taking the first row, it is actually taking the first column - [3 5].