Both 問い合わせ and 依頼 can mean to ask, but my co-workers are using both words in the application we are working on as if they are two different words.
I have a suspicion one is transitive and one is intransitive in their usage, but not entirely sure.
Edit: From the comments an enquiry and a request are both asking for information. That is where i was getting confused.
The two words mean different things. They just happen to be different things that can sometimes be represented by a single English word.
問い合わせ is a request for information. You often see it used for customer support phone numbers you can call if you have questions about the product you just bought.
依頼 is a request for someone to do something (such as provide you with a service), often also translated as "commision". It's the word you use if you ask a lawyer to represent you, hire a freelance design firm to make you a web page, etc.
