Read from left to right down the lines:
Pokeball, Great Ball, Ultra Ball, master Ball, Safari Ball,
Level Ball, Lure ball, Moon Ball, Friend Ball, Love ball,
Heavy Ball, Fast Ball, Sport Ball, Premier Ball, repeat ball,
timer ball, nest ball, net ball, dive ball, luxury ball,
heal ball, quick ball, dusk ball, cherish ball, park ball,
Pokeball-Standard ball for catching pokemon
Great ball-Slightly better version of the poke ball.
Ultra Ball-Slightly better version of the great ball.
Master ball-Guarantees the pokemon will be caught.
Safari ball-Pokeball used in the safari zone.
level ball-More effective against pokemon lower leveled than yours.
Lure ball-Works better against pokemon hooked by a fishing rod.
Moon ball-Works better against pokemon that evovle by means of a moon stone.
Friend ball-Any pokemon caught by this will start off with 200 value happiness.
love ball-Works better against pokemon of the opposite gender.
heavy ball-Works better against heavier pokemon.
fast ball-In the old games, fast ball works against pokemon who try to flee, and in the newer games, it works better against pokemon with at least base 100 speed.
sport ball-The pokeball used in the bug catching contests. Originally called the Park balls.
Premier ball-Works exactly like a pokeball.
repeat ball-works better against pokemon you've already caught.
Timer ball-Works better when more turns have passed.
Nest ball-Works better against lower leveled pokemon.
net ball-works better against bug and water pokemon.
dive ball-works better against pokemon found underwater with dive.
Luxury ball-Helps pokemon gain happiness faster.
heall ball-No added effects, but restores the health of a pokemon caught.
quick ball-Catch rate is high, but only good during the first turn of a battle.
dusk ball-works better at night or in areas like caves.
cherish ball-The pokeball used for event pokemon.
park ball-Used for pal park catching contests.
dream ball-the pokeball used in the dream world.