First off a definition of a low energy transfer orbit;
A low energy transfer orbit is...
- An orbit that allows transfers between two central bodies (e.g. earth - moon).
- An orbit that does so using energy from a source other than the spacecraft (most commonly perturbations due to the sun).
A high energy transfer orbit basically doesn't satisfy point #2 above.
The reason the these types of orbits are typically discussed in reference to transfers between two central bodies is due to the requirement of the second central body to capture the satellite. This is different to a simple change in semi-major axis around a single body as the changes due to perturbations typically act over a much, much longer period of time (think years+ for significant differences in most cases*). When there is a small perturbation as you're approaching a second body things get a little more complicated. This might help:
XKCD Gravity Wells
Looking at gravity wells, you can see there are peaks between all objects. If you imagine your satellite as a marble, you could roll up a peak with a given energy X but not quite make it over the peak - you would fall back toward the planet you left. But if there was a small amount more energy, let's call it w, then you might just make it over the peak.once you're over the peak you fall into the gravity well of the next body. Now if we say we need 100 energy (let's forget about units for now) to get to from body 1 to body 2, clearly X was less than 100. Maybe it was 99, maybe it was 95, but either way it wasn't enough. w however was tiny, maybe ~1% of X... so roughly 1 energy. Luckily 99+1=100 so we made it. That is a stripped down version of how low energy transfers work - it gets more complicated when you're talking about 3 body systems (earth - moon transfer in a sun system for example), since the specifics of the orbit need to play to the strengths of solar perturbations, but you get the idea.
A Hohmann transfer orbit is actually a high energy transfer orbit, in that it is higher energy then the low energy transfer orbits. It is the most energy efficient transfer orbit if you ignore perturbations and outside sources.
For further reading (and as a reference to this answer) I would suggest: Low Energy Transfer to the Moon.
*This can depend on what types or changes you're looking for. Drag will be exponentially more significant the lower your perigee altitude; solar radiation pressure is less altitude dependant etc.
Named transfer orbits are hard to come by. Hohmann transfers are reasonably low energy but in this context they are considered high energy - to be clear here;
Any transfer orbit that doesn't benefit from energy from external sources (e.g. solar perturbations, etc.) is considered high energy. A Hohmann transfer is simply the lowest energy of the high energy transfers (best of the worst).
Transfers that include areobreaking could also be considered low energy, as you gain the thrust to retard the spacecraft motion from a source other than the spacecraft (drag) but practically speaking you can't reliably areobreak into a stable orbit (once you start areobreaking, you're on a collision course with the planet one way or another unless you do another burn.
I haven't heard of this being done, but in theory I would imagine you could use a gravity gradient stabilisation system to reduce the energy required. The oscillation due to the stabilisation would provide a source of energy assuming you moving toward/away from your central body. This is important as a change in inclination (ignoring zonal harmonic effects) would not cause there to be a change in the stabilisation oscillation.