Just to add another option to your growing list of answers xD
"scribe" means to write, inscribe is usually used when handwriting is used, hence the other answers talking about "writing". You can simply write on or you can carve into the surface.
Engraving as said before means to cut/carve/indent, and doesn't have any connotations to handwriting like inscribing does.
So to recap: Inscribe: handwriting + can include carving, can include symbols.
Engrave: carve/cut/indent design or text + can include handwriting.
So you can see that the definitions overlap and can be interchanged in some situations. :)