Note
The words Menschen and Leute are almost synonymous.
die Leute is more casual and more frequently used. It describes the people around you, society, neighbours, people in the street, people in general... it could translate as folks, guys... it occurs in expressions as ' What will the people think', 'the rich people' , 'the posh people', 'the people want more money' 'the people are wondering what is coming next', 'the people are waiting'...
Menschen refers to human beings. A doctor should not talk about 'Leute'. In general when talking about sick people we would choose 'Menschen'. It is used when opposing man to animals, when talking of the exploits of mankind (the first men to travel to Mars ), when pointing out the weaknesses of men (Sie sind auch nur Menschen. - They also are only human beings /don't expect of them what they cannot do), when talking of disasters or wars were men are afflicted, when outlining that somebody behaves nicely/ is helpful (Endlich mal ein Mensch. - Finally a human being)
Also 'Menschen'is the only of the two words with has a singular form.
der Mensch - the person