Both games are 4X space games, so they share a genre and theme, so I don't think it's too big of a surprise that these games are similar. But there are a lot of differences between them.
Some people on the Distant Worlds forum might even find it an insult that you think they're nearly the same!
It just depends on how fine/sensitive a filter you are comparing the two. But I can think of two immediate, glaring differences: 1) game setup, in Stellaris you spend points on creating your own race, DW you choose from existing ones; 2) the way colony control is done: DW is very hands off, just tax a maybe a few facilities, whereas Stellaris has the pop growth in different regions which you micromanage.
"There's nothing new under the sun" -- Stellaris is bound to look like a lot of its predecessors in this field (DW, MoO, GalCiv, etc.)