In Harry Potter and the Order of the Phoenix, after Umbridge has dismissed Trelawney, the teachers get her trunks back upstairs by using “Locomotor Trunks!” However, wouldn’t this same thing have been accomplished with a simple Wingardium Leviosa?
Locomotor is specifically to move things.
Locomotor seems to be a spell used specifically to move things to other locations. Tonks used it to move Harry’s trunk of Hogwarts supplies from the Dursleys’ house out to her broom.
Harry’s trunk rose a few inches into the air. Holding her wand like a conductor’s baton, Tonks made the trunk hover across the room and out of the door ahead of them, Hedwig’s cage in her left hand.”
- Harry Potter and the Order of the Phoenix, Chapter 3 (The Advance Guard)
Presumably, as it’s a spell intended specifically for moving things from one place to another, it’s relatively easy to lift and control the movement of heavy objects with Locomotor. Also, Locomotor only seems to levitate objects a few inches off of the ground, unlike Wingardium Leviosa, which can levitate them much higher. Moving objects from one place to another doesn’t require them to be levitated high up Having the objects only a few inches off the ground is actually likely to be better for moving them, as they won’t fall from the sky and pose a potential danger if the spell doesn’t go as planned.
Wingardium Leviosa is a levitation charm.
Wingardium Leviosa is meant for levitating things. When Professor Flitwick introduces it to his Charms class, he says they’ll be making objects fly.
“Even better, Professor Flitwick announced in Charms that he thought they were ready to start making objects fly, something they had all been dying to try since they’d seen him make Neville’s toad zoom around the classroom.”
- Harry Potter and the Philosopher's Stone, Chapter 10 (Hallowe’en)
Wingardium Leviosa can be used to move objects, but it’s not its main or intended use.
“Ron looked around, then directed his wand at a twig on the ground and said, ‘Wingardium Leviosa!’ The twig flew up from the ground, spun through the air as if caught by a gust of wind, then zoomed directly at the trunk through the Willow’s ominously swaying branches.”
- Harry Potter and the Deathly Hallows, Chapter 32 (The Elder Wand)
However, though it can be used to move objects, Locomotor is likely a more effective option, as it’s intended specifically for that purpose. As Wingardium Leviosa is intended for levitation, not moving things from one place to another, it may not be as easy to control the motion of objects lifted by Wingardium Leviosa as it would be to control its motion using Locomotor instead. Additionally, the only objects lifted with Wingardium Leviosa whose flights are clearly directed by the caster are relatively light, like the twig and Nifflers that are levitated into Umbridge’s office. It’s likely to be even more difficult to control heavy objects, like trunks, lifted by Wingardium Leviosa.
"Locomotor trunks" is merely an adaptation. The word "locomotor" is simply used to designate motion, and the word "trunks" is used to designate the objects. Thus, "locomotor trunks" causes trunks to move. Compare this to the leg-locker curse mentioned in Philosopher's Stone:
"Now don't forget, it's Locomotor Mortis," Hermione muttered as Ron slipped his wand up his sleeve.
"Mortis" means death in Latin. So this incantation simply means that movement should be dead, i.e. the leg-locker curse.
Presumably, any wizard with sufficient skill could perform any number of spells with the base "locomotor". You would only be limited by your creativity and magical ability.
Note also the generic description when Parvati and Lavender are studying for O.W.L.s in Order of the Phoenix:
and Parvati and Lavender, who were practicing basic locomotion charms, were making their pencil cases race each other around the edge of the table.
There are yet other forms of spells that can also cause locomotion in objects. In Prisoner of Azkaban Hermione moved a tree:
Somewhere above him, Hermione whispered, "Mobliarbus!"
The Christmas tree beside their table rose a few inches off the ground, drifted sideways, and landed with a soft thump, right in front of their table, hiding them from view.
Later in Prisoner of Azkaban a similar spell is used to move Snape's body:
He muttered, "Mobilicorpus." As though invisible strings were tied to Snape's wrists, neck, and knees, he was pulled into a standing position, head still lolling unpleasantly, like a grotesque puppet. He hung a few inches above the ground, his limp feet dangling. Considering that "corpus" is Latin for "body", and "arbus" is close to Latin for "tree", we can assume that "Mobiliarbus" and "Mobilicorpus" simply make bodies and trees mobile. And again, presumably this could be expanded based on a wizard's creativity and ability.
Wingardium Leviosa is described in Philosopher's Stone as making objects fly:
Even better, Professor Flitwick announced in Charms that he thought they were ready to start making objects fly, something they had all been dying to try since they'd seen him make Neville's toad zoom around the classroom.
Obviously, the motion of flying can be controlled, as Flitwick did with Neville's toad. So what then is the difference *if there is one) between Wingardium Leviosa and other spells?
Well first of all, the other spells don't seem to be flying spells per se. They are spells that give motion to otherwise stationery objects, and while perhaps that motion might include a bit of flying (or at least hovering), theya re not fundamentally flying spells.
Note also one other spell that includes the word "locomotor". In Deathly Hallows McGonagall used this spell on the suits of armor:
“And now – Piertotum Locomator!” cried Professor McGonagall.
And all along the corridor the statues and suits of armor jumped down from their plinths, and from the echoing crashes from the floors above and below, Harry knew that their fellows throughout the castle had done the same.
“Hogwarts is threatened!” shouted Professor McGonagall. “Man the boundaries, protect us, do your duty to our school!” Clattering and yelling, the horde of moving statues stampeded past Harry, some of them smaller, others larger than life. There were animals too, and the clanking suits of armor brandished swords and spiked balls on chains.
Here "locomotor" seems to be more than just granting motion. It seems to be granting a degree of sentience to the objects, such that McGonagall can tell them once what to do and not have to continuously be magically directing them. This can be applied to the trunks as well. When casting "locomotor trunks" the caster simply tells the trunks (whether verbally or not) where to go, and the trunks go there on their own.
Contrast this with Wingardium Leviosa, where continued focus is apparently important. When Malfoy lost his focus during his exam in Order of the Phoenix, his object fell:
Out of the corner of his eye, Harry distinctly saw Malfoy throw a scathing look over at him; the wine glass Malfoy had been levitating fell to the floor and smashed.
Additionally, in Deathly Hallows when Harry used Wingardium Leviosa on the sidecar we are told that he couldn't do much more than simply keep it airborne:
In desperation Harry pointed his wand at the sidecar and shouted, "Wingardium Leviosa!" The sidecar rose like a cork, unsteerable but at least still airborne.
It's not entirely clear why it was unsteerable, given that we have seen other instances where Wingardium Leviosa could control a flight pattern. It's possible that it had something to do with the height, the size of the object, or Harry's inability to properly focus under the pressure.
In short, incantations seem to be pretty fluid and are really just the way that the wizard channels his magical will. The locomotor series of spells that we see in the book seem to be more along the lines of telling an object what to do, while Wingardium Leviosa seems to be more of a controlled flight.