probably not

IDK how much you read, but you definitely skipped chapters, or didn't bother to remember story building. I'll kindly remind
tower = stats, skill proficiency (higher difficulty = higher rewards, more points = %completion / difficulty)
dungeon = resources, skill proficiency (money) {wasn't mentioned but skill proficiency increases by using them}

currently just mana alone he outclassed fuckface and sent shivers down his spine at only floor 21.
stats = strength, skill proficiency = technique
no matter how great and proficient a skill is, if you're too weak it'll feel like getting slapped by a feather, and without mana you can't preform the skill

As far as I recall, if you’re an awakened, you have the right to enter the tower. In fact, that’s the main indication of the possibility of becoming an awakened.

or both

It's just a little funny it would be like if in any American thing whenever they had a Japanese person they would call them like Kang chin, or "my Korean friend, Pho wing," or "my Chinese comrade Hirohito smith," it's not even really a complaint it's more so funny to notice.

i know the actual answer...i just find the juxtaposition funny. like it's always just a little wrong, like just enough to know someone thought about researching it and said "Fuck it" Instead.
like Goeden for instance "should his name be Golden, no too on the nose, maybe something that sounds close... whats the english name i heard in that drama... gideon, goebel, ... goeden Yeah that sounds right."