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".