Feuerzeug is a lighter, its a fixed term, nothing "wobbly" that relates to fire-stuff.
Zünder is an igniter/detonator, Zündung is the ignition.
Zeug can be used as "thing", but it is frequently used when refearing to gear. So "Feuerzeug" is like "Firegear", "Werkzeug" is the "gear for working" (tools).
There is Zündholz for “match” but lo[0], apparently there is/was Zündzeug:
Stuff is “Stoff” as in Brennstoff.
Fire-thing and burning-stuff.
Lighter is “Zünder“ in German.
Feuerzeug vs Zünder
To close to call regarding which is clearer.