Just thinking of these mouthpieces, which one is wider in diameter( pls. exclude rim thickness)??

They have also different shapes, and I like to research for the reasons why they are made like that. Pls. help me. thanks to all

French horn mouthpieces typically have a larger inner diameter.
Trumpet mouthpieces generally are between 15.8mm and 17.0mm
Horn mouthpieces are generally between 17.0mm and 18.0mm

Cup Shapes::
Trumpets often have a cup shape and Horn often have a funnel shape. I have seen both for either. Typically trumpets have a cup and where the cup meets the throat is where the air breaks and then flows into the instrument. This break is similar to how the flute produces it's tone, but happens inside the mouthpiece. The cup, or "Semispherical" innards match the cylindrical aspects of the instrument.
Horns are conical and their mouthpiece reflects that. The sounds is not as definiable on a V-shaped mouthpiece as a cup-shaped mouthpiece. Which is why Horns tend to blend so much better with so many instruments.

The are other aspects that affect your sound. Cup shape, throat, bore, backbore (rate and ratio), backbore flare, shank length, shank depth, etc.

There are many variables in mouthpieces that work with the construction of the instrument. Cup