This refers to the type of weapon, not that it can be a particular magic weapon.
This is explained in the Dungeon Master’s Guide, in the section Magic Item Categories:
Some magic weapons specify the type of weapon they are in their descriptions, such as a longsword or longbow. If a magic weapon doesn’t specify its weapon type, you may choose the type or determine it randomly.
Similarly for armor:
Some suits of magic armor specify the type of armor they are, such as chain mail or plate. If a magic armor doesn’t specify its armor type, you may choose the type or determine it randomly.
This is important because each enchantment has an assigned rarity to it, for example, a Weapon of Warning is uncommon. A Vicious Flame Tongue Dragon Slayer Vorpal Sword would be dope, but its rarity would be the sum (product?) of rare, rare, rare, and legendary, and I’m not sure what that even means.
To be clear, if you’re the DM and you want to give one of your players a Vicious Flame Tongue Dragon Slayer Vorpal Sword, go right ahead. If your party is level 20, balance started to lose its meaning a while ago.
The DMG does mention this possibility in Chapter 9: Dungeon Master’s Workshop:
You can also modify an item by fusing it with properties from another item. For example, you could combine the effects of a helm of comprehending languages with those of a helm of telepathy into a single helmet. This makes the item more powerful (and probably increases its rarity), but it won’t break your game.
The use case given here, Helm of Telepathically Comprehending Languages, likely won’t break your game, but your super dope sword might, so just be careful.