There are a wide variety of relationships that any pair of people can have: friends, lovers, romantic partners, friends with benefits, and many others. Often, there is even confusion between partners as to the exact nature of their relationship, such as when one person thinks that they are dating and the other thinks that they are just friends with benefits.
I look at relationships on three axes: connection (friendship), love, and physical (sexual), as show below:
Each of the relationship types that I put in the various zones are meant to be examples, not an exhaustive list of relationship types.
The point of this model is that it gives us a way to look at a relationship in order to get a more solid idea of what the relationship really is and what to expect from it. Often times, a relationship is only considered from the standpoint of two axes, which can create misunderstandings.
The Connection Axis refers to attributes of the relationship which make good friends: interests in common, ability to hold good conversations, comfort together, etc.
The Love Axis is the affection, emotional connection. If this axis is strong then each partner will want to place the needs of the other person before their own, be happy in the other's happiness on a gut level.
The Physical Axis is the simplest to understand. It is the physical connection. Unfortunately, it is often mistaken for love. Two people will be tremendously physically compatible which leads to passionate feelings, but the feelings are only about the physical connection, not the emotional.
Suzie says: I was seeing this guy, and I really thought it was going somewhere. The sex was really mindblowing, and I felt that we had a deep connection and would talk for hours. Turns out that he thought we were just a casual thing. I was heartbroken.
In Suzie's relationship, there was plenty of physical and some connection, but the love element was not there. They were really just friends with benefits. Suzie felt the physical connection and the friend connection, and mistook it for an emotional connection because she was not looking at all three axes separately.
When considering a relationship, one should consider how it lies on all three axes, and make sure that both partners agree on what type of relationship this is. The model of connection, love, and physical gives you a framework in which to discuss the relationship and what both parties might expect in it.
Being a model, it is highly abstract. It is meant to be the beginning of a conversation, not the end.