I don't understand hex grids

[Wired]

I really don't, on a very basic level. That is, I know where to find hex generators and all, so that is not what I'm aksing for. If I say "one inch hex", does that mean the hex covers one square inch? That one side of the hex is 1 inch?

To illustrate my problem:

This here is supposed to be a 12x18 inch map with an 1 inch hex grid. I've taken it from here and enlarged it to showcase my dilemma.

Yet, if I use this hex generator (which was linked from the Guild in the past) to create a 1 inch hex grid my result looks like this (mine in red):



So, am I doing something fundamentally wrong? What is it that I don't get? Are the preview maps wrong????