Does "hieroglyph" only refer to the ancient Egyptian form of writing or to any writing system whose basic elements represent words?

Egyptian hieroglyphs are the most popular, but the word hieroglyph is of Greek origin ("sacred carvings") and can refer to the characters of several other logographic writing systems:

• Anatolian Hieroglyphs
• Cretan Hieroglyphs
• Olmec Hieroglyphs

And more.

I believe the more general term is logogram, meaning a symbol primarily denoting a word (or phrase) rather than a letter. But words and letters are slippery concepts themselves, so that wouldn't be a hard-and-fast distinction.

Anyway, I'm happy enough using logogram to include Chinese pictograms, or whatever else you want to call them, as well as various hieroglyphs. But I'm not so comfortable saying hieroglyph includes the Chinese symbols.