Verified answer

-なさい is polite order. It is imperative of -なさる which is is polite way of saying "する."

-(っ)て is non polite request.

The reason one may hear -なさい often for an order is because using a verb in imperative comes out too strong and rude.

Parents might use -なさい to their kids. Hayaku kigae nasai. (Hurry up and change cloths.)

As mentioned police use -なさい, but I have heard them use verb in imperative form as well. Tomari nasai. (Stop) Tomare. (Stop).

食べてください　Please eat. (polite request)

食べて (Please) eat. (non polite request)

食べなさい Eat. (polite order)

食べろ Eat (impolite order)

なさい is still an order and looses its politeness a bit in formal situation, and you might here なさいませ to sound really polite.

/-te/ is the more common way to make polite requests, and used more in everyday conversation. /nasai/ is used a lot in requests by authority figures, such as teachers to their students or parents to their children.

- I often hear my wife say, /Maaten, okite/ (Martin, get up) the first time that she goes in to wake our son up in the mornings, but then a few minutes later she'll go back and say in a louder and less patient voice, /Maaten, okinasai!/ (Martin, get up!).

- My son used to have a little toy police car that would say as he rolled it across the floor, /Mae no kuruma, tomarinasai!/, which means "The car in front of me, pull over!".

- I've overheard teachers say to unruly kids, /Moo, damatte suwarinasai!/: "That's it! Sit down and shut up!"

Also, you may notice that the Japanese use /-nasai/ a bit more often with us "gaijin" than with each other. I don't think that most are really trying to be patronizing or condescending, but they do tend to see non-Japanese as childlike and less evolved, until they get to know you personally.

As a non-native speaker, you would be safer using /-te kudasai/ yourself.