Not to me or what I'm saying.
You're seriously going to argue that I haven't said one isn't a spell and the others are spells? Because that in my(and every other person's) book is an articulated difference between the two.
Other than being vulnerable to things that affect spells... what makes a spell different from an ability that expends a spell slot?
If being anti-magicked, silenced or counterspelled aren't it... what else is there? Yes, I get one is called a spell and the other is called an ability, but that's like arguing that halberds and glaives are completely different weapons in 5e because one is called a halberd and the other is called a glaive. Practically speaking... there is no difference in the 2014 book between the two weapons, and you've dismissed every difference between Divine Smite the ability and Divine Smite the spell as not really mattering.
They aren't equally true, though. You're making stuff up that isn't even implied, let alone stated. That doesn't get equal weight to, "It's not written there so it's not there by default."
I am not making things up, I am making observations based on how the game is played at every table I have seen and been at. Your only refutation of that is "but they didn't spell that out in the books"
And again, frankly, this is a useless point. Because it came about because you were claiming that an enemy caster might confuse the paladin for a war cleric and counterspell their abilities... but you don't even play with counterspell. So now you are arguing simply because you don't like what I've said, not for any point in the actual discussion.
The only thing left is Silence. That's it. That is the last point you have not conceded as not mattering.
According to D&D Beyond(and I disagree with their numbers) only 2% of PCs reach 11th level. That would mean that 98% of paladins never see that damage.
Oh noes! When I gave a range of possible damage numbers a paladin could give out, I gave a number that less than 2% of all paladins might be capable of! Should I go to the naughty jail for naughty people because I figured on a reasonable maximum that tens of thousands of people will reach?
More seriously, this is a red herring, not an argument. My range doesn't get invalidated just because the high-end of the range is high. That's the point of a range.