Difference between －ませんか　and ーましょか

What is the difference between －ませんか　and ーましょか？ えうがをみませんか・ えうがをみましょか・

～ませんか　is something like a "negative of invitation." Think of it like saying "won't you..." So 「えいがをみませんか」 translates to "won't you watch a movie?" ～ましょか is typically used to say "let's _____ (together)." 「えいがをめましょは」 would then be "let's watch a movie" or "shall we watch a movie?"

Elenaさん、 I　think Nytngaylさん　gave you a very good answer. Basically, ませんか and ましょうか are used to invite someone to do something. ませんか (drop ます from verb-masu form and add ませんか) means "won't you do (action)?" いっしょにパーティーへ行きませんか？ Won't you go with me to the party? Whereas, the ましょうか　means "shall we..?" いっしょに作りましょうか？ Shall we make it together? Also if you drop the 'か' from ましょうか you can use it as another way to invite someone. Lit. meaning "Let's do..." 学校まで歩いて行きましょう Let's walk to school. (lit. Let's go to school by walk）