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A FX/Full Frame body has a 1:1 in relation to Field of View (FOV).
So a 300mm (FX or DX) lens on a FX will give 300mm FOV though you may get vignetting due to the image circle being too small for a FX sensor.
A 300mm (FX or DX) on a DX camera will have a 1:1.5x in relation to field of view. So the 300 will act like a 450mm FOV.
The issue here is the zoom lens isn't zooming like advertised .. if I read all that correctly.
So a 300mm (FX or DX) lens on a FX will give 300mm FOV though you may get vignetting due to the image circle being too small for a FX sensor.
A 300mm (FX or DX) on a DX camera will have a 1:1.5x in relation to field of view. So the 300 will act like a 450mm FOV.
The issue here is the zoom lens isn't zooming like advertised .. if I read all that correctly.