Why is the input size different?
I guess it has been a mistake. Take a look at here.
The other author's were Ilya Sutskever and Geoffrey Hinton. So, AlexNet input starts with 227 by 227 by 3 images. And if you read the paper, the paper refers to 224 by 224 by 3 images. But if you look at the numbers, I think that the numbers make sense only of actually 227 by 227.
To elaborate on @Media's answer, what is meant by "I think that the numbers make sense only if they're actually 227 by 227" is the following:
In the attached snapshot, the size of the 1st convolution layer is $55x55$. Now suppose the dimensions of the input images are $224x224$, then by applying the $11x11$ kernels with $stride=4$ as described in the paper, would result in:
Whereas if the dimensions were $227x227$, then that would result in:
which conforms with the size of the 1st convolution layer described in the paper.
* I got the formula for calculating the output size from this YouTube tutorial.