difference between propose and offer

offer - (санал болгох)to ask someone if they would like to have something, or to hold something out to them so that they can take it. Offer to pay for the ice cream
1)[transitive] to ask someone if they would like to have something, or to hold something out to them so that they can take it
       ----- Can I offer you something to drink?
2)[intransitive and transitive] to say that you are willing to do something:
      ---- I don't need any help, but it was nice of you to offer.
3)[transitive] to provide something that people need or want
        ---- Your doctor should be able to offer advice on diet.
propose - (санал тавих)to formally suggest a course of action at a meeting and ask people to vote on it
Propose we go eat ice cream --Propose is the most formal.

1) [transitive] to formally suggest a course of action at a meeting and ask people to vote on it
       ----The resolution was proposed by the chairman of the International Committee.
2)[intransitive] to ask someone to marry you, especially in a formal way
      ---- Shaun proposed to me only six months after we met.

What is an Offer? | What is Proposal?

• Propose we go eat ice cream

          Offer to pay for the ice cream

• offer has an element of exchange or cost implied. For example, the phrase "make an offer" when negotiating the price of something. An offer is from some party to another party, whether you're offering your hand (to balance somebody), your house (to host a party), or a discount (on the sale of an item).                                                                                                        Propose is the most formal. You propose to your girlfriend that the pair of you get married; it's unlikely that you would suggest the same thing. The best working definition of propose I can think of is "to make a formal submission for appraisal." This is why researches write proposals for research funding and not suggestions.

          

• The words ‘ proposal’ and ‘offer’ are synonymous and are used interchangeably. Section 2 (a) of the Indian contract act defines a ‘proposal’ as, “ when one person signifies to another his willingness to do or to abstain form doing anything, with a view to obtaining the assent of that other to such act or abstinence, he is said to make a proposal”. This definitionreveals the following three essentials of a ‘proposal’.
  
  
  (i)    One person signifies to another; it must be an expression of the willingness to do or to abstain from doing something. According to section 3 to signify means that the proposal must be communicated to the other party.
  
  
  (ii)   The expression of willingness to do or to abstain form doing some thing must be to another person. There can be no ‘proposal’ by a person to himself
  
  
  (iii) The expression of willingness to do or to abstain from doing some-thing must be made with a view to obtaining the assent of the other person to such act or abstinence. Thus a casual enquiry “ do you intend to sell your motorcycle?” is not a ‘proposal’. Similarly, a mere statement of intention” I may sell my motorcycle if I can get Rs. 14,000 for it” is not a ‘proposal’. But if M says to N, “ will you buy my motorcycle fro Rs. 14,000,” or “ I am willing to sell my motorcycle to you for Rs. 14,000”, we have a ‘proposal’ as it has been made with the object of obtaining the assent of N.
  
  
  
  The person making the ‘proposal’ or ‘offer’ is called the ‘promisor’ or ‘ offeror’, the person to whom the offer is made is called the ‘offeree’, and the person accepting the offer is calledthe ‘promisee’ or ‘acceptor’.