As far as I can tell, there are three different ways that "natural weapons" are described:
Talons: You are proficient with your unarmed strikes, which deal 1d4 slashing damage on a hit.
Cat's Claws: In addition, your claws are natural weapons, which you can use to make unarmed strikes.
Hooves: Your hooves are natural melee weapons, which you can use to make unarmed strikes.
There also already exist the following two questions which explain that these wording differences do matter:
- "Do natural melee weapons (from racial traits) trigger Improved Divine Smite?"
- "What are natural weapons?"
How do these different classifications work with the booming blade spell, which states:
As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell's range [...]
Which races, if any, could use their unarmed strikes with booming blade?
Please know I am fully aware of the technicalities and differences between melee weapon attacks, and attacks with weapons, and that regular unarmed strikes count as the former but not the latter.