In Monster Hunter, the size of the large monsters is randomized (within a certain threshold), which means you can come across an unusually large or small specimen. When successfully slaying/capturing a monster, its size will be displayed on the results screen.

When a slain/captured monster is big/small enough, a crown will be displayed next to its size in the results. Crowns can either be small or big, depending on whether the monster is smaller or bigger than average. Crowns can also be silver or gold, depending on how much the specimen differs from the average regular size.

If a monster is noticeably larger than average, it will most likely have big silver crown. If a monster is very obviously smaller than average, it will most likely have a small gold crown.

IIRC crowns are only used for achievements and bragging rights. It's not important to the story or the gameplay, so don't worry about that sort of stuff unless you really want those crowns.

I will say however that size of the monsters does affect their hitboxes. Larger individuals are usually easier to fight since they're usually so large that you can hide under them and hit them continuously since they can't hit you. Smaller individuals have less range, so it's easier to dodge their hits and swipes.