The distinction lies between "Melee weapon attack", and "Attack with a melee weapon".
It gets worse. There is also a difference between "attack with a ranged weapon" and "make a ranged weapon attack." Throwing a dagger counts as the latter but not the former.
I don't consider this worse. This is an exact parallell - neither making it worse nor better.
The problem is the phrase "weapon attack."
Well, sort of.
The genesis of the confusion, of course, is that it was only AFTER release they came up with the Monk errata. Before errata - when unarmed was just another weapon - there was nothing awry with the phrase.
It simply means "a physical, as opposed to magical, attack". (There are attacks. They can be weapon attacks and they can be spell attacks. A monk kicking an Ogre in the head is clearly not the latter, and so it is the former)
If they had bothered to fix the Monk issue properly, instead of the present quick and dirty fix, we wouldn't have this conversation.
What I mean is, they could have kept hands and feet as "weapons" and instead made exceptions whenever it doesn't make sense for these limbs to follow a weapon-related rule. For instance, if it really is that important to prevent you from combining a natural weapon with, say, two-weapon fighting then
say so for that particular feature. Yes, it's more involved, but a heck of a lot easier to understand: "natural weapons are weapons except where noted". Other cases to be determined include frenzy; various strikes, smites, and styles; retaliation, battle and war magic, disarms; weapon enchantment spells like Magic Weapon or Holy Weapon... just to mention some.
Or, they could have distinguished between "weapon attacks" and "unarmed strikes", and then amended every rule to match this. Whenever the PHB talks about weapon attacks and mean only attacks with weapons, nothing changes. (In many cases, the language already says "melee weapon attack" for instance. In those relatively few passages where it talks about weapon attacks and Monks are included, the language is amended to instead say "weapon attacks and martial strikes". For instance, the rule about moving between attacks (PHB190) says "If you take an action that includes more than one weapon attack, you can break up your movement even further by moving between those attacks." It could easily say "If you take an action that includes more than one weapon attack or unarmed strike, you can break up your movement even further by moving between those attacks or strikes."
Generally, the fix comes across as sloppy. I am not at all convinced the Monk is so overpowered it needs to be barred from each and every instance of multiclassing synergy. Just as I am convinced
some instances are too good, I'm convinced not all of them needed to be shut down.
The situation is entirely one self-inflicted by the designers.