One key difference is that the focus is on working on the PRESENT in to the FUTURE.  Where are you now and where do you want to be?  Successful people use coaching to gain more success in their lives - whatever ‘form’ that success may take, ranging from financial to happiness...
It is a positive, powerful and purposeful construction of your life as you would LIKE IT TO BE. Life Coaching is about Living on Purpose, with Purpose.

At the risk of being annoyingly general: ANYTHING that they want more success / satisfaction in.  Some examples are Career: change or advancement; Health and Wellbeing: from weight loss or stress management to work-life balance; Relationships and Communication: including enhancing existing relationships (partners / parenting/ colleagues); attracting new ones; building confidence; team dynamics; and even how to make the most of retirement...You get the idea.

It’s actually easier to answer that from the ‘who wouldn’t benefit’ angle. In reality coaching isn’t for everyone. Sometimes it is more appropriate for someone to deeply process and heal the past before being fully able to focus on creating an inspiring future. Counselling has a more relevant place for that need.

Also, I’ve been known to refer to ‘uncoachable’ people (sorry not very pc). What I mean by that is, sometimes, even though a person may genuinely believe they want to grow and move forward in some areas of their lives, they are actually quite ‘happy’ being miserable. Literally there is too much benefit in their current (stuck) situation to really commit to shifting it. Someone needs to be willing to move forward in order to be ‘coachable’.