You might enquire, or ask about, the difference between the words enquire and "inquire." Good question. The answer is, not much. They are the same word with different spellings. Typically the British prefer the "e" version, but both are correct.
When you enquire about something, you are asking a question. This can come in many forms. Sometimes when you enquire, you are doing an investigation of a crime or an unsolved mystery. The National Enquirer is a tabloid that investigates celebrity gossip. But enquiring doesn't always have to be so dramatic. You could just be enquiring about the time.