If I was your parent I would think it feels like running away. And it would not make me feel better. You may not think this is important, but it is very important. You should ask yourself a few questions...what will this do to my relationship with my parents? What will this do to my relationship with my friend? Am I doing this because of a temporary issue or something that is deeper? Is there a different solution? This action may have outcomes that you are not anticipating. Think it through very carefully before taking this step. Talk it through with a counselor or an adult that you trust. This is a far more important issue than you think.
When ever some one is leaving home with out telling their parents not where they are going,yes its running away. But you may want to look at why you are and see if there is somethng that can be done about it. I say that as it'smy quess is your very young,and perhaps to many kids run away often because they dont communicate well enough with their parents,or simply dont like the rules.Not saying that in this case,but something to think about.
I wouldn't say the definition is something you need to worry about. You are planning on leaving home and that can have certain legal and financial consequences, depending on your age and circumstances. I'm really hoping you've had a really good, hard think about this. This may mean severing the ties with your parents permanently. Is the situation at home at the point that you are unable to maintain your normal functioning? Is the toll it has on you mentally setting you up for destruction later on? If there is any hope of saving your home life, it might be worth a chance. Things are going to get hard if you follow the route you've chosen, in different ways to now, but they will be very hard. The choice rests with you as to which stress is more bearable for you. Is the family that you will be living with aware of your situation? Are they going to welcome you and be ok with supporting you emotionally as well as financially? Look into what your options may be in your area for financial and emotional support. See a counselor if you haven't yet, maybe through school or a youth aid service. They will be able to put you in contact with the kind of people and resources you will need. Your situation sucks, I have no doubt about it. But if at all possible, before you leave, try to have a plan in mind to look after yourself. There is nothing worse than having to choose between going back home or surviving on the street. It might take a little more pain, it might take a lot. It might take a few extended stays living with your friend so you can get a clear head. But please please do this right the first time.