There are already some posts talking about inquiry, enquiry, and survey.
However, a real sharp definition and distinction between survey and inquiry words is still missing and I'd like to be sure about their differences and best uses.
English Language & Usage Stack Exchange is a question and answer site for linguists, etymologists, and serious English language enthusiasts. It only takes a minute to sign up.Sign up to join this community
Martin Beckett's answer uses both words in a different sense from the way I understand your question, so I have a different answer.
Assuming that you are asking in the context of a sizable investigation into something:
an inquiry is a process in which individuals are summoned or invited to give their evidence, opinions, preferences and arguments: generally individuals who know that they something to say on the matter.
a survey is a process of asking the same set of questions of a number of people, who may or may not have much interest in the matter. It can also be used of collecting and comparing information about a number of products or services.
Aside from any narrower/technical meanings of the words, such as "marketing survey" or "court of inquiry", I would use "survey" to indicate that a more comprehensive knowledge is the aim. An "inquiry" would be more likely (but not exclusively) to be focused on resolving a particular question, while a survey would aim toward comprehensive knowledge of a subject area in its entirety.
For example, a book's subject matter might be:
a survey of pre-Civil War US history
an inquiry into the causes of the American Civil War
Survey would be to study a range of items/options while inquire is more specific.
"I surveyed the range of TVs on the market" - "I inquired/enquired about the Sony model XXXX"
edit: Assuming this answer Enquire and inquire we decided that you mean enquire (in the AE sense)