In short:
- Is inventor Aaron W. Salter the same man as 2022 Buffalo shooting victim Aaron Salter Jr? Yes.
- Did Aaron Salter have a patent related to efficiency of hydrogen-power engines? Yes.
- Did Aaron Salter invent a car that runs on water? Absolutely not.
Was he the same man?
Aaron Salter had a Linked In profile that shows he was both a police officer in Buffalo New York and linked to his company AWS Hydrogen Technologies.
I have been a police officer for the last 27 years the last two I have been in the traffic division, I do the events at the First Niagara Center along with riding the motorcycle doing parades and races around the city of Buffalo. I'm a jack of all trades a master of none I'm always working on my vechicles and or my project of running engines on water for the last four years or so, I would like to realize my dream of getting cars to run off of water using my newly discovered energy source some day.
Images provided by the victim's family, e.g. in People Magazine match this YouTube interview of the inventor:
in which he explains he is a Buffalo police officer.

Did he have a patent?
Aaron Salter had a patent, filed in 2015 and granted in 2018: Method and system for using the by-product of electrolysis.
An engine system for generating hydrogen and oxygen, and a method using a by-product of electrolysis, for use in an internal combustion engine to improve efficiency and reduce emissions. The engine system has an electrolysis cell for generating hydrogen and oxygen by electrolysis of an aqueous solution, a battery as a source of power for providing electrical power to the electrolysis cell, and cooling system for maintaining the temperature of the electrolysis cell to reduce problems associated with overheating of the cell during electrolysis. [...]
The patent has expired because fees were not paid.
Does this engine run on water?
In summary, this invention takes some water and a full battery, and ends up with hydrogen, oxygen, some sludge (from water impurities), and a flat battery. The claim is that the sludge can be used to make a hydrogen engine more efficient than other hydrogen engines.
This is not running an engine on water. It is essentially running on a battery. There is a cycle of turning water into hydrogen and oxygen and then back to water again.
In the above interview, he describes building a prototype of an "HHO" fuel system, where the hydrogen is mixed into the fuel intake of a gasoline engine. We have addressed HHO engines on Skeptics.SE before. They do not run on water.
He also describes a system where he ran an electrolysis cell (off a gasoline engine) until he built up enough hydrogen pressure to be able to run the car off hydrogen for several minutes. Again, this is not running off water. The fuel of the overall system is gasoline.