If you can't tell the difference between being the strongest at anything and finding Laugh Tale you shouldn't waste your time with reading this series.
One is changeable and not stable, we've seen Oda clearly doesn't care about the titles or hypes, and anything is possible in a fight. While you find Laugh Tale, no one can take it from you again. Even if another person finds it again. One is a feat, other is a hype.
Feat is beating someone. Zoro wants the title, he wants the hype. He doesn't care who he beats as long as he achieves his goal. Mihawk doesn't need to be that person specifically, another person can have that title/hype and Zoro can beat that person.
One is changeable and not stable, we've seen Oda clearly doesn't care about the titles or hypes, and anything is possible in a fight. While you find Laugh Tale, no one can take it from you again. Even if another person finds it again. One is a feat, other is a hype.
Feat is beating someone. Zoro wants the title, he wants the hype. He doesn't care who he beats as long as he achieves his goal. Mihawk doesn't need to be that person specifically, another person can have that title/hype and Zoro can beat that person.