If I understand this correctly, any attack made with claws, teeth, tails, is considered a weapon attack (for the purpose of determining the attack type), because the creature is using its natural weapons. So any spells and effects that would benefit a weapon-attack, benefit a natural weapon.
Correct. Claws, teeth, tails, and other body parts are not categorized as spell attacks, so they must be categorized as weapon attacks, since those two categories are the only ones the game rules cover how to make.
But this is different from physical weapons, in other words: objects, such as sword and clubs. Spells that benefit a weapon, or object, do NOT work on natural weapons, since they are technically not actual weapons (as in: objects).
Correct. So when a spell like
magic weapon says "You touch a nonmagical weapon." you can't choose Steve, or a goat, on any other creature, because none of those are nonmagical weapons.
So could we say that Unarmed Attacks are only made by creatures that could wield physical weapons, but decide not to use them, and use their hands and feet instead?
Almost.
Some creatures which could wield objects as weapons, but decide not to do so, still have natural weapons that they would use instead of making unarmed strikes (a weretiger in hybrid form using it's claws, rather than scimitar or longbow), and other creatures which could wield objects as weapons, but decide not to do so, have natural weapons that they have been specifically allowed by the game rules to use them to make unarmed strikes (the PC versions of lizardmen, and tabaxi, in Volo's guide).
So there are three categories of creatures that could wield physical weapons, but decide not to use them:
1) Those that have natural weapons to use that do not count as unarmed strikes (Monsters)
2) Those that have natural weapons to use that do count as unarmed strikes ("monstrous" PC options)
3) Those that do not have natural weapons, and thus fall back on unarmed strikes by default
Though this is a point at which I would deviate from, and encourage deviation from, what the game books actually say in favor of a more simple ruling despite whatever consequences it might have that could be considered "unwanted": all of category 1 above are treated as if they were category 2.