Is there a line between professional coaching and life advice?

There is definitely a line in the sand, but the two can potentially overlap. My personal opinion is that what you do in your personal life and professional life (habits) shows up in both. 

Yes there is a line and in my opinion a very clear one. When reading the question I immediately thought of the adage, "Bring a man a fish...Teach a man to fish..."; coaching teaches people who to fish.

The role of a coach is not to impart anything. Coaches facilitate, through questions, the individual becoming self-aware of their potential to successfully act/resolve/influence an outcome and as a result of their self-awareness become intrinsically motivated to follow through. Advice describes imparting guidance or recommendations on what to do now or in the future in support of a potential outcome; although at times, and in certain instances necessary, it is directional by nature. 

In my experience, Mentoring and Coaching are often put into similar buckets.  Good coaching is focusing on the individual and the topic or agenda that they want to dig into (work or personal).  There may be personal influences that are affecting the professional or the same in reverse.   So long as the individual seeking the coaching is driving the conversation.  The coach is there to bring awareness and provoke deeper thinking.  Mentoring (again in my experience) tends to be more advice, knowledge sharing and focused more on professional advice.  

Yes, there is a line that can easily be crossed or blurred.

It's a virtual line that I see gets more blurred as time goes on, because work and life impact each other so much. It's more about helping people grow and living a fulfilling life. Someone once said to me that “success without fulfillment is failure”. And so it’s important to regularly evaluate where we are in life in terms of our purpose, our goals, what and who is important to us, and so on. 

There used to be this notion of work vs life balance. But in my opinion, you have to view it more holistically. I believe that if you're looking after yourself emotionally, physically, mentally, and spiritually, you will be more successful professionally. I don't think you can silo off those two things, your performance at work is impacted by what’s happening in your personal life and vice-versa. For example, I was informally coaching a highly intelligent professional with a very stressful, high-risk job. After about 3 months and a lot of conversations we made some adjustments that made both work less stressful, and home life more enjoyable. The thing is this is always a work in progress. I believe that as we progress in our professional lives and take on more responsibility, the need for a good coach becomes even more important.