numpy: "size" vs. "shape" in function arguments?

Shape relates to the size of the dimensions of an N-dimensional array.

Size regarding arrays, relates to the amount (or count) of elements that are contained in the array (or sometimes, at the top dimension of the array - when used as length).

For example, let a be a matrix

1  2  3  45  6  7  89 10 11 12

the shape of a is (3, 4), the size of a is 12 and the size of a[1] is 4.

Because you are working with a numpy array, which was seen as a C array, size refers to how big your array will be. Moreover, if you can pass np.zeros(10) or np.zeros((10)). While the difference is subtle, size passed this way will create you a 1D array. You can give size=(n1, n2, ..., nn) which will create an nD array.

However, because python users want multi-dimensional arrays, array.reshape allows you to get from 1D to an nD array. So, when you call shape, you get the N dimension shape of the array, so you can see exactly how your array looks like.

In essence, size is equal to the product of the elements of shape.

EDIT: The difference in name can be attributed to 2 parts: firstly, you can initialise your array with a size. However, you do not know the shape of it. So size is only for total number of elements. Secondly, how numpy was developed, different people worked on different parts of the code, giving different names to roughly the same element, depending on their personal vision for the code.