Company wise, the answer is no. They are two completely separate companies. When it comes to other things, yes.
The relation between Neopets and Marapets among players of both sites, is based on the fact that the founders of Marapets, were Neopets users at the time they founded the site.
When Neopets started to become famous (around 2003-2004, before Viacom bought the site in 2005), many other virtual pet sites had appeared such as Zetapets, Subeta Pets, Power Pets, etc. All of them based in the same main features the Neopets site had to offer: Owning a virtual pet, feeding your virtual pet, playing games to earn points to be able to feed your pets, to morph, to paint, to dress, or to costume, etc. Out of all of them, Marapets has been so far the most successful to evolve after Neopets, with members totaling over 5 million currently. Originally, founded by two teenage users of Neopets back in 2004.
It's quite interesting how this unravels. If you want to learn more about why some people believe that Marapets and Neopets are related, take a look at these sources: