We spend so much time and emotional and intellectual energy worrying about things we can't change. If we free up all that mindspace, think of what we can achieve.
You can't control what someone else thinks or does. Once you choose to free yourself of this concern and focus on yourself and the impact you can have in your world, your stress level will reduce considerably. I know, I’ve done it.
Both are really important at certain times in your life, but the differences are many.
Mentoring and advising are wonderful ways to gain support and advocacy, as well as learn from the experience of others. They are important aspects of a professional network, and can be formal or informal. Mentors may have their own agenda in terms of knowing what is right for you, or wanting you to serve their organization in a particular way. Sometimes requesting mentoring can be political, it can be a great way for someone who can help with your career to notice you. But be aware, if this is your only motivation, the mentor will smell it and feel you are wasting their time.