AF-S 18-300mm 3.5-6.3 vs AF-S 55-300 1.8-5.6 : Confusion about image magnification between the two

darrob

I'm very new to photography.
About a year ago, I got a D5600 with the 18-55 lens.
Very shortly after that, I go the 55-300 mentioned in the title.
Quite happy with that, although I got frustrated with the very long AF time, missed a lot of shots of birds in flight.
After doing a fair amount of reading, a lot of sole searching and finding the right special price, I managed to get the 18-300.
I had thought that I would get a lens with the reach of the 55-300 but with the twin benefits of faster AF and getting down to 18 if I wanted landscapes.

I've run into a real issue, however. I'm not certain if I don't understand how lenses work, if there's something wrong with my lens or I'm going crazy.

It seems that my 55-300 has a higher magnification than my 18-300.
I have taken shots with the 18-300 at 70, 100, 200 and 300 mm and compared them to the same shot taken with the 55-300.
In every case, the subject is larger (at every focal length) in the shots taken with the 55-300
I would go so far as to say that the shots taken at 200mm with my 55-300 is about the same as the ones taken at 300mm with my 18-300

Has anyone here noticed anything like this at all? Is this normal or do I need to be talking to Nikon about this?

Any comments/help would be appreciated