Between 发财 and 致富, which one is more commonly used? Or is there any difference in emphasis.
发财 is informal, vulgar sometimes, simply means you get a lot of money.
致富 is formal, largely used by CCP media, no one use it in conversation.
致富 is a verb that's closest to "wealth creation", usually in the business or trade context. So both gambling wins and earning money from professional service (e.g. as a medical doctor) wouldn't be associated with 致富. 致富 implies wisdom, smart or cunning in money matters.
发财 is somehow receiving money or value that's slightly unexpected or associated with luck or if not luck the amount is more than usual. So picking up $10 on the street maybe "发财了" is fit. Being a medical doctor or lawyer, if described as "发财" it would imply a hint of jealousy or contempt on the part of the speaker. "发财" is morally neutral, so both a con job or receiving an inheritance can qualify. Anyway it is informal speech.
About the "Which one is more commonly used?" note that there are many other similar terms which are appropriate for different situations. 赚钱 is most common and neutral, including receiving salary for hard work or smart business.
I happened to learn it a few days ago in my class, and my teacher explained 发财 is more used in oral context while 致富 is used in a written context (书面语).
发财is informal, like "make big money". Depending on the context, it may sound uneducated.
致富 is formal.
致富 is a process to be rich. 发财 is a result to be rich.
致富 means you are not a rich man now. If you want to be a rich man, you have to find a way to be a rich man. The process is called 致富。
发财 means you've already got a lot of money. you are wealthy. In Chinese, 你发财了.