It looks like (if I've parsed right) every one of them stands for "Earth", except that HEO alone can also be overloaded three ways (high-earth, highly-elliptical, and highly-eccentric).

This is unimportant, but: a site:nasa.gov search shows all three "HEO" acronyms in common use, there; and even Wikipedia abbreviates it inconsistently across entries[0-2].

https://en.wikipedia.org/wiki/Medium_Earth_orbit ("A medium Earth orbit (MEO) is an Earth-centered orbit with an altitude above a low Earth orbit (LEO) and below a high Earth orbit (HEO)")

https://en.wikipedia.org/wiki/Highly_elliptical_orbit ("A highly elliptical orbit (HEO) is")

https://en.wikipedia.org/wiki/High_Earth_orbit ("In this article, the non-standard abbreviation of HEO is used for high Earth orbit[2]")

[edit]: I overlooked the abbreviation of "geostationary equatorial orbit" for GEO, which brings it up to four different "E's"!