What is the difference between a general and an admiral?

Question

On screen we see:

• General Solo lead a ground assault against Endor.
• General Calrissian participating (or leading) a fighter assault against Death Star 2.0
• Admiral Ackbar commanding rebel capital ships in the battle around Death Star 2.0
• General Kenobi participated in many ground battles during the Clone Wars, but also commanding officer of the Open Circle Fleet.

In the Legends we see:

General Garm Bel Iblis, who initially commands his own fleet of around 6 Dreadnaughts. He ultimately becomes the supreme commander of the New Republic, coordinating many space battles, but remains a general.

Grand Admiral Thrawn, who commands the Emperial forces, command space faring battles, but also coordinates several ground based assaults.

Those are only a few examples of the confusing history of mixing General and Admiral roles in the Star Wars universe.

Answer 1

Ultimately, the answer to the question comes down to the source of the officer's commission. Admiral is a Navy (also Coast Guard in the US) rank and General is an Army (also Air Force, Marine) rank. The rules for command of mixed service forces vary widely from country to country and situation to situation, but in almost every situation the overall commander of a particular force is supposed to be chosen based on the needs of the force's mission. Every country with multiple services has a system for equating the different ranks of those services so that seniority in a multi-service operation can be clearly and easily established.

Depending on the legal code of a particular nation, it may be difficult or even impossible to transfer an officer from one service to another, or it may simply involve more paperwork than the higher level command feels like processing. This could lead to odd situations such as generals commanding navy forces.

At least, that's the way it is in this place we like to call "reality". In a fictional setting, where none of the precise details are available (because they aren't necessary to the telling of the story), it can be impossible to know why a particular character is assigned his or her given rank.

Answer 2

What stands out in your question is that the Admiral is in charge of the "fleet" and the Generals are in charge of Air or Ground forces supporting a re-skinned amphibious landing: from space, not from water, onto planet/land. This is a standard trope in space opera and sci/fi. (A stellar example is Heinlein's Starship Troopers, the book). The author overlays a real life landing from the sea to land onto the futuristic attack/raid from space onto a planet¹

As to Generals being in charge of ship to shore attacks, or space to shore attacks, the RL model for that is the Marines, and for that matter General MacArthur running his series of Amphibious Operations in WW II. The "inconsistencies" you note reflect the analogous mixing of roles IRL in Joint Operations at the highest military ranks. It's no big deal, and has a basis in real world history.

Writers write best when the write what they know.

All of these tropes and story telling conventions were around long before George Lucas began telling stories and making movies.

The convention / trope of using Navies / Fleets / Admirals in sci fi and space opera stories predates World War II. You can see that in E.E. Doc Smith's sci fi stories. (Smith was first published in 1928). Other writers who established the most common tropes as sci fi moved from pulp fiction into movies include Robert Heinlein and Larry Niven, both of whom used fleets and navies for starships/spaceships.

This "fleet/Admiral" theme became canon in TV as well: Star Trek "Starfleet Command" is hopefully familiar to most fans of the Star Trek series and movies. They applied a trope that was already decades old.

Using "General" for those in charge of the soldiers/ground forces landing on the planet fits the above as well, as with whomever is in charge of the Air Force, (as above, Lucas being an American would tend to default to American usage) would be a general. Again, Lucas is an American, and their ships have planes (aircraft carriers) so you'd not be surprised to see an Admiral in charge of a bunch of planes launched from a space fleet's major vessels.

The creative mind behind Star Wars, George Lucas, was very familiar with Hollywood and WW II movies that saturated our cinemas for about 40 years and certainly when he was growing up.
(Experience point here: Lucas (born in 1944) is about 15 years older than I am. I saw dozens of WW II themed films growing up, including a lot of old black and white films that would have been new when Lucas was at a similar age).

George Lucas would know reflexively that an Admiral is in charge of the ships carrying the invasion/raid force, and a General would be in charge of the troops, but he'd also know about high ranking flag officers (Generals and Admirals) were in charge of Major Operations. (Eisnehower in charge of the Normandy Invasion, MacArthur in charge of an amphibious campaign in the pacific, Admirals in charge of invasions of Tarawa and Iow Jima ...)

Sci Fi is a form of speculative fiction which takes what we know and reskins it somewhat. George Lucas wrote what he knew. He would also be comfortable with how, at high ranks, a General or an Admiral is in charge of all of the forces, air sea and land: example include Admiral Nimitz, General Eisenhower, General MacArthur ...).

To answer your question in another way:

A decades old trope was embedded in the style of story Lucas told, a story created by a man who grew up reading sci fi stories and watching Hollywood movies laced with the distinctions between the Navy carrying soldiers/Marines and the Generals in charge of troops, but the "Big Brass" being of either origin. This wasn't original, and it should come as no surprise.

¹ If you play StarCraft, they use the same tropes, but they do mix and match a bit with "General Duke" and "Admiral Stukov" seeming to play the same role for different sides. I guess the folks at Blizzard read the imperatives for Joint Operations and Joint Command structure in 1986 Goldwaters Nichols act and folded that in.