An Enquiry (pl. Enquiries) is also known as a Lead or a Prospect. It is typically a person who has exhibited a preliminary interest in the services or products that you sell. At this stage you do not know what is the timeframe when this person will buy, whether he/she has an approved budget or even if he/she is the right person within the customer organization and can influence or make the purchase.
A Deal (pl. Deals) is also known as an Opportunity. Once an Enquiry or Lead is qualified and you know about the budget, decision time-frame and other aspects of the prospective customer, you can convert an Enquiry into a potential Deal. A Deal has it own set of stages through which it goes before it is either won or lost.
A Contact (pl. Contacts) is also known as a Business Contact. It can be anyone you know and are in touch with professionally. An Enquiry may convert into a Contact at an appropriate stage.