That must be it. I kept watching the two clocks to try and figure out if the second was equal but couldn't. This is the key and should be the first thing you read, seconds not being the same length is a huge detail.

Strange the page does not describe the "metric second" then, since it is not the same as the SI second. I thought that the second was the unit which was the same as in SI (=metric). But then it is not the same as the SI second, so not metric at all. Very confusing.

I feel it's an error to use the same names in the two systems. The values are different, it would be much less confusing to use names that are clearly different too.