I received an email from IndiGo stating "Your IndiGO Itinerary". Should I ask them for a ticket? I have no idea. Can you please let me know what the difference between itinerary and ticket is?
Itinerary is a route of a journey or a sequence of different rides/flights between different stops which build a journey on this route.
Ticket is a document (it need not be a piece of paper, it may be in electronic from, f.e. as a QR-code on your smartphone) which allows you to take a transport on your itinerary or on a part of it.
In your case, if you have paid for a ticket and there is a booking/ticket number, you most probably have recieved your ticket.
Itinerary: "The part of the PNR describing the flight segments booked for the passengers named in the name field of the PNR."
Ticket: "The document entitled “Passenger Ticket and Baggage Check” issued by or on behalf of the carrier and includes Notice of Contract Terms Incorporated by Reference and notices and the flight and passenger coupons contained therein. The document may be paper or electronic."
[Source: IATA Recommended Practice 1008 "Glossary of Commonly Used Air Passenger Terms".]
To paraphrase a little, an itinerary is a list of flights you are presently booked on. A ticket is a contract entitling you to travel. You can have one without the other: you can book flights and ticket them later (typically through a travel agent or in person at an airline ticketing desk), and you have a ticket that is open for use without any particular reservations being made for you on any flight (although this is now rather unusual).