Hey :) Both words are right to use for "Christmas tree". But I guss the word "Weihnachtsbaum" is more common.

"Christbaum" is more common here in Austria

Every year In winter, the Germanic tribes herded their cattle along evergreen branches because they believed that good spirits were at home in the branches and brought good luck to the animals. The Christians probably liked the idea too - and from century to century more and more Christmas trees were put up. In the 17th century, the first candles were placed on the branches and in the 19th century, somebody had the idea to hang glass balls on the branches. Originally the tree was called "Christbaum" and religious people still do this today (especially in Southern Germany). But also many non-denominational people celebrate Christmas and so the name "Weihnachtsbaum " was born and it’s very common to call the tree like this today.

Das ist eine persönliche Entscheidung. That's a personal decision. Ähnlich wie bei den Weihnachtsgeschenken: Similar to Christmas presents: Bei manchen Familien bringt sie der Weihnachtsmann und bei anderen das Christkind. (Auch wenn es eigentlich die Eltern sind ;-))))) In some families they are brought by the "Weihnachtsmann" and in others by the "Christkind". (Even though if it's in reality the parents ;-))))) Manchmal hat es auch etwas mit katholisch/evangelisch oder Süden/Norden zu tun, aber das stimmt eben nicht zu 100%. Sometimes it has to do with katholic/protestant or with south/north, but that doesn't fit to 100%. Also bleibt es bei der persönlichen Entscheidung... Therefore it stays a personal decision...