What is the difference between wollen and möchten ?Feel free to just provide example sentences.

1) Both verbs express a wish or a demand. You say what you want or like to do or what you want somebody to do.
Ich will/möchte ein Eis.
Ich will/möchte, dass du jetzt nach Hause gehst.

However "möchten" is more polite than "wollen". "Wollen" is very demanding and strong.
Children who are crying and screaming because they want to get an ice-cream and their mother says "No" usually scream "Ich will ein Eis!!" NOT "Ich möchte ein Eis."
=>
Ich will ..... (I want)
Ich möchte .... (I would like to...)

2) there is an important difference concerning grammar. Even though both are modal verbs "möchten" is different to "wollen" in that it only has a Präsens form but no other forms like an infinitive, participles or a Präteritum-forms.
If you want to express "möchten" in other tenses you have to use the forms of "wollen".
Ich möchte ein Auto kaufen.
Ich wollte letztes Jahr ein Auto kaufen.

What is the reason for that?
"möchten" is actually not a full verb by itself but is the subjunctive 2 form of "mögen" which has gained a meaning different to the original subjunctive 2 meaning.