My enjoyment of stories involving artificial gravity on a space craft has always assumed that it was not actually gravity of some kind (maybe it's tricks of inertia, force fields, etc), exactly for the reason you propose. The ability to create actual gravity fields would have far reaching effects, and some of them devastatingly dangerous.
We first need to discuss how real gravity works. Gravity is a natural property of all matter. All matter attracts to all other matter. The weird part is that it's an extremely weak force, except as more matter clumps together, the gravitational force increases. More massive objects exert more gravitational force than less massive objects. It's even weirder that gravitational force between two objects increases as the distance decreases. Two objects approaching each other propelled only by their gravity will accelerate as they get closer together. This is why gravity is expressed in distance per time squared.
It's not necessary to go into the exact math (mostly because I don't understand it, lol), but it's necessary to know that gravity is based on mass, is stronger with more mass, and is exponentially stronger with linear decreases in distance between two objects.
For true artificial gravity, there's really only one conception: an exact point in space that, with respect to gravity, imitates the center of mass of an object. In the plainest understanding, the machine targets a point in space that then attracts all other matter to that point with an actual gravity field.
Where it gets tricky (meaning, using such tech effectively), is that gravity is mathematically tied to the mass of the object. If you wanted to lift by gravity with the same force as earth's gravity, then you'd need a massive point that matches earth. But suddenly dropping an earth weighted point in the solar system would have obvious devastating effects. In fact, it would be so bad that the only use for that would be to destroy planetary environments.
Where it might be an actually usable technology is if it's possible that a mass can be big enough that when in close proximity it would attract nearby objects at greater than planetary gravity, but would not be massive enough that it would meaningfully affect the planet itself. To make this truly useful, this technology would have to be able to move the artificial gravity point so as to keep a consistent pull on the target object. So I imagine a massive point, with virtually no volume, that you can place in extremely close proximity to an object, and as that point pulls the object, you move the point in your desired direction.
Depending on your readers, maybe you can hand-wave this as possible. To actually find out, you'd really have to ask a physicist. My lay-understanding has me believing that the math would punch out unfavorably. It would be intensive pull at only a few millimeters, and virtually none at only a few centimeters. If we put such a force above your head, it'd be more likely to make you dizzy before actually lifting you in the air.
So anything you lift would need a specially designed harness. The harness has a bit of mass which is the target, and when it moves, it pulls by attachments your actual target object. You couldn't just grab whatever you want. Every "gravity move" would require planning and preparation. Lifting an Earth built space station would require a very small mass, like a golf ball, that could attach to and then lift the entire station. Sounds unlikely, so you'd have to add like a thousand golf balls all over and inside the station, and then target them all in unison. Holy crap, this is getting complicated!
But if it's possible, then all the terrible side effects go away. That's great!
Another interesting use would be propulsion, both on planet and in space. You could put this tech in virtually every vehicle, provided the vehicles are designed to have the target "golf balls".
