Mohenjo Daro is a real name, it actually belonged to the Harappan Civilization and archaeologists have found ample evidence of a flourishing town near the banks of the Indus river. Buuuut, whatever happens in that village is an entire work of fiction. Disagree? Well if you think that really people in Harappan civilization used to wear fine print clothes and there were horses and the princess used to wear headgears like she just got out of a Vogue magazine's Spring Summer collection, you're horribly mistaken. Also, I'm sorry you had to go through an atrociously stupid interpretation of history.

Similarly, the village of Champaner in Lagaan was an imaginary village which was shot in Kutch, Gujarat. The village was prepared fo the shoot but for the most part of it, it was already there. Hence, the first similarity was the basis of both of them being shot in imaginary backgrounds, taking cues from real historic events. But, you must be thinking this does not qualify as a parameter to claim they are both just one and the same. Agreed, that's why now we'll address the elephant in the room( or is it a unicorn? Guess, we need to call up Mr. Gowariker).

Bhuvan is introduced in the film with a sequence of deer, whom he is trying to save from Gunshots. Whereas Mohenjo Daro starts with a shot of a unicorn drinking water from a river. Errr... It took 15 years for Mr. Gowariker to take the leap from Deer to unicorns, impressive. At least someone came up with a different imagination. (Sigh)

Yeah, it's not the entire story, obviously. Like if the directors really worry about taxes and the oppression of people going on, how would they put in songs and drama which will make people hoot? So yeah basically, just like Lagaan was a movie about cricket, Mohenjo Daro is about History. But the cue in both films is the  tax. Bhuvan stands up against the British oppressors so that they exempt the village Champaner from Taxes, and similarly, Sharman stands up against the Chief of Mohenjo Daro (Maham) because he decided to put more taxes on people from the lower city. Bhuvan and Sharman both lead the anti-tax takedown of the government. (Yayyy! Who knew politics could be interesting in films, eh?)

While we would expect that the filmmaking and storytelling will change a bit in the 15 years that have passed, it turns out to be wishful thinking. The villain in Lagaan , Lakha (played by Yashpal Sharma) is after the girl (Gracy Singh) and loses his temper when she chooses to go with the hero ( LOL, very unexpected). Similarly, the unrequited love trope in the film Mohenjo Daro is still alive and well when the villain Moonja (played by Arunoday Singh) goes batshit crazy when he finds out that the flower-crowned princess is in love with Sharman. 

The teeny tiny difference is that Lakha just betrays Bhuvan, Moonja throws Sharman in front of two Dutch-looking Bigfoots who wield creepy weapons.

The story claims that they are man-eaters from mountains, but they look more like campers on Prozac. With bad teeth.

In Lagaan, Bhuvan stands up and claims "To fir alag alag saari ungliyan ki mutthi ban jaayi Mukhiya JI" when asked about how will he fight to remit the taxes.  Eerie similarity can be spotted in the film Mohenjo Daro when Hrithik (Sharman) stands up in the same fashion and claims "Jo ungliyaan khuli thin, unhein mutthi banane ka samay aa gaya hai". 
I mean, leave out the visual similarities, even the dialogues ring the same bell. 

The language in Lagaan is a mix of Bhojpuri, Avadhi and Hindi. Which is not authentic, but understandable for the audience. Also, in Mohenjo Daro, the first few minutes are spent in incomprehensible language which then turns into a concoction of something really close to the rural dialects spoken in parts of UP and Bihar and Sanskritised Hindi. Just so you know, it contains words like 'Hamaalkhor' and 'Soon' (which means Sona = Gold. Okaaayyy then.)