What do these two creatures have in common, aside from the fact that the latter turns into the former when Harry sees it? Well, a lot, actually.
Boggarts are a physical manifestation of fear. They look like giant spiders for Ron, dementors for Harry, and Professor McGonagall telling Hermione she failed all her classes, but they always take on the worst fear of the person facing them. They are defeated by the ridikulus spell, but the spell on its own means nothing. It’s laughter that defeats a boggart; all the spell does is morph one’s fear into something that can be laughed at.
Dementors are cloaked monstrosities that suck the hope and happiness out of the world around them. Unlike boggarts, they are not considered easy to defeat; while Professor Lupin teaches his third year students how to fight boggarts, he warns Harry that the magic used against dementors is far more advanced. However, much like ridikulus, it is not enough to simply shout “Expecto patronum!” and wave one’s wand. The Patronus Charm is fueled by happy memories, the very things that dementors drain away.
In other words, laughter is to a boggart what happiness is to a dementor. Both are dark creatures that represent a very real negative emotion, and both are stopped not simply by magic but by an equally real positive reaction.
Let’s take it a step further: Voldemort, the greatest evil in the Harry Potter series, is defeated by love. It is Lily Potter’s sacrifice, made out of love, that protects baby Harry and defeats Voldemort the first time around. Later, at the end of the fifth book, Dumbledore tells Harry that the line in the prophecy about “power the Dark Lord knows not”, refers to Harry’s ability to love, which is something Voldemort cannot even begin to comprehend. He himself is cold and unfeeling, and he constantly underestimates the things that others will do for love, eventually leading to his downfall.
Hate and evil can only be defeated by love. Despair can only be defeated by holding on to happy memories. Fear can only be defeated by finding a way to laugh at it.