Enquire and inquire are very close in meaning, and in many contexts either word is acceptable. Both can mean to ask for information.
A common distinction is this: enquire is often used for general questions, while inquire is often used for formal investigation or official questioning. For example, you might enquire about train times, but a panel might inquire into an accident.
Regional usage also matters. In British English, enquire is often more common for everyday asking, while inquire appears more often in formal contexts. In American English, inquire is generally the more common spelling for both everyday and formal uses.
- General question: I enquired about the cost of the course.
- Formal investigation: The agency will inquire into the safety failure.
- American English: Many writers would use inquire in both sentences.
If you want a simple rule, use enquire for everyday asking in British English, and use inquire for formal investigations or for most contexts in American English.