At 300mm will the magnification of a 28-300mm lens be the same as a 70-300mm lens?
Nominally, on the same camera (same crop factor), it should be the same, if focused at infinity. But most lenses exhibit an effect called focus breathing, i.e. they change their focal length when focused at a shorter distance.
The nominal values (28-300 or 70-300) are only true at infinity. How much focus breathing a given lens exhibits can only be found in test reports, maybe, it's not data given by the lens manufacurer in the data sheet.
The job of the camera lens is to project an image of the outside world onto the surface of film or digital image sensor. The size and shape of this light sensitive surface defines the camera’s format. The focal length of the camera lens is the fundamental property of lens. This value the key factor we use to gauge the resulting image as to its angular filed. In other words, “normal”, “wide-angle” or telephoto.
The focal length tells us about the power of the lens. We are talking about how big or how small (magnification) an object will image. Magnification is linear. If an object’s images 1mm height with a 50mm lens mounted, a 100mm lens magnifies 2X more so the project image will be 2mm. mount a 200mm lens and the image height expands to 4mm. How does a 300mm lens relate to a 50mm. We divide 300/50 = 6. This translates to: a 300mm projects an image 6X larger than a 50mm. Thus the same object is now projected as an image 6mm in height.
Focal length is a distance measurement. Provided we use the same unit, such as millimeters, this fundamental lens property is universal. In other words a 300mm projects an image that be the same size as any other 300mm lens. Yes there may be minor differences because of accidental or deliberate misstatement of the focal length. This slight variation is of no significance and likey comes from finding the exact location of the rear nodal or intentional rounding of the actual value.
In addition to “focus breathing”, stated focal lengths are rarely accurate and are usually rounded up or down.
Popular Photography tests each lens for focal length accuracy in their reviews and show both the specified and tested focal lengths.
Here are some examples from Popular Photography:
Canon 70–200mm (68.72–193.94mm tested)
Nikon 70–200mm (69.41–200.02mm tested)
Tamron 70–200mm (68.68–196.11mm tested)
Sigma 70–200mm (70.01–200.08mm tested)
Tokina 70–200mm: (71.21–200.02mm tested)
Tamron 28-300mm (28.89-297.11mm tested)
Nikon 28–300mm (27.99–290.65mm tested)
The field of view should be the same given that the lenses are used on a camera with the same size of sensor. Although most lenses that reach a certain round focal-length (300mm) are rounded so the actual focal-length may be 292mm or 301mm.
More so many lenses change focal-length slightly as they focus. Manufacturers usually specify the focal-length assuming infinity focus. So even if a 300mm is actually 302mm at infinity, it may become 288mm at 2m (random numbers for illustration).
Magnification is something related but usually refers to the minimum size of an object that it can image covering the whole field-of-view. This is impacted by the minimum focus-distance of the lens and its field-of-view (determined by focal-length and sensor-size). So two 300mm lenses, even if they actually are 300mm may have entirely different magnification depending on their optics. If one focuses down to 2m while the other to 1m, magnification will be about twice as much on the one that focuses to 1m.