They're different, but when these words are said out loud it's hard to tell them apart. A parody is a silly spoof and parity is equality, and that's no joke.

A parody turns making fun of something into an art form. Imitating the way someone talks or writes is a parody. Broken down into its Greek roots, it's para for "beside," and ode as in "song," which forms paroidia for a "burlesque song or poem." A parody isn't as risqué as a burlesque, but it's definitely supposed to be funny. Here are some examples of the word:

"He's also a professed fan of the 1960s spy parody ‘Get Smart.'" (Washington Times)

"The online parody shows a player pretending to be J.J." (Los Angeles Times)

"From a Saturday Night Live hosting gig to a parody Twitter account, the ‘Girls' star is everywhere." (Time)

When there's parity, things are even-steven. Parity means equality. It even has Latin roots in par, which means, of course, equal. If a scale is balanced, there is parity.

It's used in finance:

"She said she thinks the euro will fall below parity against the U.S. dollar in the coming year." (Wall Street Journal)

In social contexts:

"None of this started out as a fight over gender parity, but now that it looks like one, you can be sure women will notice."

And sports:

"In most seasons, parity usually expires some time around November as the league's usual suspects take control." (Wall Street Journal)

They word parody probably has more fun than parity, which just likes to even things out. But there is parity between these words; they are both awesome.