An offer according to section 2 (a) of the Indian contract act 1872, "when one person signifies to another person his willingness to do or abstain from doing anything with a view to obtain the assent of that other person it is said to make an offer / proposal.
Example:- A wants to marry B he asked to B that will u marry me?
Here A is making a proposal /offer to b with a view to obtain her assent.
While invitation to offer :- it is made with the intention to negotiate or offers to receive offers are known as invitation to offer.
Example:- An invitation by a company to the public to subscribe for its shares. Here the company can accept the application of shares or can reject them.

Offer:
An offer is a proposal made by one party to another party with the intention to create a legally binding agreement. It is an expression of willingness to enter into a contract on certain terms and conditions. The offeror must communicate the offer to the offeree, and the terms of the offer must be clear and definite.

Invitation to Make an Offer:
An invitation to make an offer, also known as an invitation to treat, is not an offer itself but an invitation for others to make an offer. It is a preliminary stage before the actual offer is made. It is an indication that the party is willing to receive offers but does not intend to be bound by them.

Key Differences:
1. Intention:
- An offer is made with the intention to create a legal relationship and be bound by its terms.
- An invitation to make an offer is made with the intention to invite others to make an offer, but not to be bound until a valid offer is accepted.

2. Communication:
- An offer must be communicated by the offeror to the offeree.
- An invitation to make an offer is usually made to the public or a specific group, and it does not require individual communication.

3. Terms:
- An offer must contain clear and definite terms, including the subject matter, price, quantity, and other essential details.
- An invitation to make an offer does not contain specific terms and is open for negotiation.

4. Legal Consequences:
- Acceptance of a valid offer creates a legally binding agreement between the parties.
- Response to an invitation to make an offer is not an acceptance but an offer in itself, which may or may not be accepted.

5. Revocation:
- An offer can be revoked by the offeror before it is accepted, except in cases where an option contract exists.
- An invitation to make an offer cannot be revoked as it is not an offer. However, once an offer is made in response to the invitation, it can be revoked before acceptance.

6. Examples:
- A shop displaying a price tag on an item is an invitation to make an offer.
- A customer offering to buy the item at the displayed price is an offer.

In conclusion, an offer is a definite proposal with the intention to create a binding agreement, while an invitation to make an offer is an invitation for others to make an offer. Understanding the distinction between the two is crucial in contract law as it determines the legal consequences and obligations of the parties involved.