This is a great question! And I'll bet it is different for everyone.
A friend - someone who you can have a laugh with, talk about the weather, basically chit chat with, but never real close.
A Good Friend - someone you can have a laugh with and maybe even get silly with, without feeling uncomfortable. Someone who you can depend on for a quick ride to the market or bank when your car has broken down. You known each others kids, families and what a lot of their likes an dislikes are.
A Close Friend - Someone you can trust with some of your secrets. They won't talk about you behind your back in negative ways...they won't spill your information to others you don't want to know. You can walk into their house and make a cup of coffee because you know where everything is kept and you don't have to wait to be asked (and vice versa too!) Their kids call you mom (or dad) and your kids call them mom (or dad). You can vacation together for a week and not grow tired of one another.
A Best Friend - Someone you can call and cry and cry and cry to when something goes wrong. Someone who can share the good times and bad and know exactly how you feel. They know you inside and out and what makes you tick. They don't judge you, but they will always tell you the truth even if it hurts a bit. You can both finish each other's thoughts and sentences.
That's my take on your question about friendship
One point I would like to make and I hope you don't mind.
All kinds of friends do not always stay in our lives. As much as we may want them to, things change. People grow at different rates, their interests change, their perceptions of themselves as well as us change. While I may be sad or angry when I loose a friend for whatever reason, down the road I am grateful for what they brought to my life when they were here with me. Good or bad, it's all a learning experience!
xoxoxo
Jean