Can someone please explain the fundamentals in elevation and gradient of climbs/hills.

There are quite a few good hills around here but I never manage to find out exactly what gradient they are (unless they are signposted).

The route below shows the maximum grade as 12.7%



Yet, a section of the exact same route (below) shows the maximum grade as 24%.



Why is this and how is the factor reached? I may be missing something simple but it baffles me

TIA