Town authority vs town influence over a tile

[metablaster]

There are 2 API's named differently that appear to do same thing (unless I'm wrong)

• AITile::IsWithinTownInfluence (or AITown::IsWithinTownInfluence)
• AITile::GetTownAuthority

What's the difference between "town authority" and "town influence" in respect to a tile?

Don't these 2 terms mean the same, that is, if tile is within influence or authority it would affect all of the following:

• Local authority rating (actions allowed in town if something is done to tile like building stations or demolishing stuff, trees etc.)
• The servicing quality of the station would influence the rating of the town
• Planting trees would increase local authority rating

Or do they mean/affect different set of rules?