Great, thanks for that clarification. So now my follow-up question, specifically the applications for wildlife photography.
I understand that for a full frame 70-300mm lens, the effective cropped focal length will be 450mm at the long end. But this is a bit misleading (right?), since physics dictates that the actual optical properties of the lens is unchanged.
How does this crop factor get applied in the field when zooming in on furry animals at a distance?
It doesn't. Its Still a 300mm lens. It behaves as a 300 mm lens. You get teh Dof you would get from a 300mm lens.
What you get in pixels, is the same as if you took the photo with 300mm as it IS a 300mm lens.
The only difference is that a crop-sensor camera chops 1/4 off the top, bottom and sides of the 'frame', compared to a 35mm 'full-frame' camera.
The clue is in 'CROP Factor'
What you get is the same 'frame' as if you had a full-frame sensor and 'Cropped' it in any other manner; masking the frame before shot; or taking printed photo and cutting top bottom and sides off it, or did similar in a digital photo-editor, or in days of dark room; putting 5x4 bit of printing paper under the enlarger, but instead of printing edge-to-edge the whole frame 'shot' on the neg, cranked the enlarger head up to enlarge the photo 1.5 times, which would require a 6x8 bit of paper, to get the whole frame in, BUT left smaller 5x4 printing paper under, so you only got the middle bit.
The 1.5x 'crop factor' equivilency, is a little abstract, and is reffering to the effective field of view you get, diagonally, corner to corner of the frame.
The 16x24mm 'crop-sensor' is half the area of a 24x36mm 'Full-Frame' Sensor; however, the liniar dimensions are aprox 1.5x longer on Full-Frame. So, if you do the geometry to work out the angles of view of different length lenses, and by 'similar triangles', you get the same angle of view from lenses also 1.5 times longer in focal length.... hence you get aprox 1.5 times 'effective' magnification from the same length lens on a crop sensor; however, back to the dark room 'cropped enlargement', you aren't actually getting that maginification from the LENS, but from magnifying smaller captured image by a greater degree in the enlargement, or on a computer screen to be the same viewing size.
Make more sense? Or completely confounded you?
Far away furry things? Would be bigger in the view-finder with 300mm lens on DX camera than 300mm lens on FX camera, about the same size as 450mm lens on FX Camera.
For same aperture; Depth of Focus around furry thing would be the same, on 300mm lens on either DX or FX camera. Same aperture on FX camera and 450mm lens, you would probably have less DoF around your furry thing, given same camera to subject distance.