For example, Diamond makes the X700HNA which is stated as a 4x5/8 vertical on 2m. Does this just mean that it is 20/8 wavelength long vertical? Or is there some magic to phasing the 5/8 segments? I'm familiar with colinear dipoles, but they normally have some sort of phasing connector (typically looks like a "hairpin" in my experience). Maybe that's just hidden inside the fiberglass, but I'd be curious if anyone has any idea what might be inside an antenna like this.
It's probably a coaxial collinear antenna.
Each segment of the antenna contains two coaxial conductors (inner and outer). At each joint, the inner conductor of one segment is electrically connected to the outer of the next, and vice versa. The center conductor in each segment forms the phasing line for the two adjacent segments, and does not radiate since it is shielded.
Typical designs of such an antenna specify half-wavelength segments, not 5/8, though.
It is possible to construct such an antenna by taking cut sections of coaxial cable and inserting the center of each under the shield of the next (while separating or insulating the shields from each other); this is a popular “homebrew” receiving antenna design for some applications.