Upvote for the main thought, but

1. A gasoline engine is a type of motor. You are making a distinction without a difference. A motor is just something that produces mechanical motion. Motor. Motion. Motivate. All come from the same root as “move”
2. An “engine” can be the whole apparatus that does the work, not merely the thing that provides the power, and could be powered by a water, beast, or even manually such as the cotton [en]gin[e]. A lot of that usage comes from pre WW2, but it survives in things like “train engine” (the vehicle that pushes or pulls a train) and “game engine” (the program architecture that manages the processing power provided by the computer to convert user interactions, game assets, etc. into something that we recognize as a game).
3. It’s not a four-cycle engine. It is a four-stroke engine: each piston makes four strokes each complete engine cycle.

Enginecycles? If you specifically refer to internal combustion engine (ICE) then it'd make sense to call them icecycles. It sounds weird, maybe icicles?

But seriously EU has a definition of what an ebike is, it's not just a bicycle with motor, there's max allowed power, max assistance level, and importantly it should only assist when pedalling. Anything beyond that, yes, is classified as a motorbike.

I'm a bit triggered by this, so let me apologize in advance for the incoming rant.

You might be kind of right etymologically, but bikes, e-bikes, motorcycles, and likely in the near future e-motos, are specific things defined by law. The confusion between these vehicle classes is causing harm.

An e-bike is a pedal powered bicycle with an electric motor that assists the rider while pedalling up to 25km/h. You might be able to switch modes between more assistance and less assistance but there is no throttle.

If you purchase a cheap walmart / k-mart bike, swap the rear wheel with a powered hub from alibaba and strap on a battery from temu, that's not an e-bike. They have a throttle and no limiter and in most cases can propel a 12 year old idiot at 50km/h but some times more than 70km/h. This is not an e-bike and more accurately described as an unregulated electric motorbike.

The frame isn't built for this kind of stress, and the riders often have no capacity to understand the danger they're imposing on themselves and others - zipping past kids playing and so on.

It's an emerging disaster in Australia and I imagine other places as well. It's turning the population against e-bikes when they're not the problem.

We urgently need more appropriate legislation drafted to clearly define the classes of vehicle, and we need police with the right skills and equipment to enforce those laws.

Really? Because I don't remember pedaling my Honda 750.

OP thinking he cracked the code to ride a motorcycle on the sidewalk.

Isn't it the electric equivalent of a moped?

Is an e-scooter a motorcycle?

Upvote for the thought.

Great video by Fort9 about this topic

https://www.youtube.com/watch?v=m-DnpTjE0ck

Depending on State, a small enough engine on a bicycle doesn't count as a motor vehicle.

I live in south east asia and motorbikes are the dominant transporation tool here and yes fast e-bikes are absolutely motorbikes. They would be treated here the same way and law wise but the adoption is very low because compared to a motorbike it's mostly a meme/entertainment vehicle as good ol motorbike is far superior and actually cheaper vehicle.

Not all the time. My engine cycle has a three cylinder 2 stroke. It's scary fast.

This is actually a really good one.

Etymologically speaking, "engine" means any invention, whereas "motor" means specifically something that makes things move. A gasoline engine is a motor; an electric motor is an engine.

Not all motos are 4 stroke. My buddy rides a two stroke KTM and that thing cooks.

The difference is in power and control. Ebikes are speed capped. There are two types, pedal assist and throttle control. Pedel assist are ones that only turn on the motor when you are pedaling. Throttle control ebikes are speed capped even more than pedal assist. I think they should be banned because of jailbreaking and it puts you in the mental state of operating a machine rather than pedaling a bike.

Also, the engine on enginecycles is a four-cycle engine.

Electric motorbikes are a thing too.

Not actually sure on this one, because the terminology for motorcycles is... Weird.

Motorcycles are what we're all thinking of, Harleys, Kawasaki's, Yamaha's, etc. Mopeds and scooters look the same, and both usually have manual transmissions, but have a floor in them. I don't know that there's a word that encompasses both, much less including ebikes? Maybe motorbike

Really unfortunate this classification system has happened. What you're thinking of is an electric moped, but it's all getting lumped together. Check this out.

https://youtu.be/bB6hBLmBhPA

Uh, no. Maybe check the definition of a word before you accuse people of using it wrong?

Besides, there is literally no benefit to this kind of approach. The most popular use of a word is the definition of the word, not the other way around. And yes, this means it will change over time. So even if motor didn't literally refer to a certain type of engine, the definition of the word motorcycle is not dependent on the definition of the word motor. Even if there was a contradiction between the definition of the two words that's literally irrelevant. There's no point getting all annoyed about it, that's just how language works. But you will not help anything by trying to force people to change how they're using a word. It'll just cause confusion and make communication even less clear.