¹ A 'self-framing' pet door frame will wrap from the inside of the installation to the outside. Thus, the core of a hollow door or wall is 'framed out' by the pet door making installation considerably easier. Any 'self-framing' pet door will have an adjustment range. Be sure that the thickness of the material you are installing in falls in this adjustment range. If you have a solid wood cored door a self-framing pet door is not required though you may still use one for aesthetic reasons.
² Plastic framed pet doors are generally less expensive and will not corrode in a salt environment. Metal framed pet doors are more strongly built. Metal extrusions are stronger than stampings.
³ Two-part flaps consist of a central flap with an additional U-shaped gasket piece that overlaps the flap and frame on one side. As these tend to be heavier than the single flap doors, they can be expected to be somewhat more wind-resistant. As well, they would be less suitable for sharing between different sized pets (large dog and a cat, for example).  A 'double' flap, by contrast, would consist of two separate flaps separated by a dead-air space for improved insulation and wind resistance.
⁴ Separate locking covers are required when the flaps are flexible. Rigid flap pet doors usually incorporate a locking mechanism in the frame which engages the flap. Some rigid flap pet doors offer a '4-way' locking device.
⁵ You may find a more appropriate fit in an unusual situation from a manufacturer offering more sizes.
⁶ Some companies produce a pet door primarily intended for cats. They tend to be more square in shape (lower aspect ratio) than a more conventional size and, so far, they all have rigid flaps. We've never heard a cat express an opinion one way or the other; but these are very popular among cat owners.