Hello dcig
Welcome to the German forum!
"Reis" is an old word for "Zweig", thus "twig". So, "Tannenreis" is a fir twig. This word "Reis" is neuter, whereas the "Reis" that is "rice" is masculine.
Ich koche den Reis.
Ich stelle das Birkenreis in die Vase.
Edit: I found a related thread, about "
Reisig".
Das Reisig is a group/bundle/number of twigs, whereas
das Reis is the single one.