Difference between "artifact" and "artefact"

Is there any usage preference between artifact and artefact?

My understanding was that an artifact was properly applied to physical, historical objects, while an artefact was more correct for more abstract, intangible, error-ish concepts, for example a compression artefact.

However, the couple of online sources I checked suggested that the difference was merely spelling, and that both were usable for both definitions.

The only usage preference I'm aware of is that artefact is preferred in British English and artifact is preferred in US English, but that both are acceptable in either case.

See the Oxford Dictionary, for example.

Personally, I tend to mix them the same way you do: I collect artifacts in Tomb Raider and my compressed photos have artefacts!

You are right. There is a slight difference in meaning, and Wiktionary makes a note:

There may be some value to distinguishing "artifact" (a man-made tool or object) from "artefact" (an false signal in data caused by the processing).

Or, in better terms, but the Science Dictionary:

Artifact: An object produced or shaped by human craft, especially a tool, weapon, or ornament of archaeological or historical interest.

Artefact: An artificial product or effect observed in a natural system, especially one introduced by the technology used in scientific investigation or by experimental error.

But they are generally used to mean "an archaelogical find".