The relationship between Emma and Harriet is an interesting one. They certainly have a friendship of sorts, but they do not meet as equals. Both Emma and Harriet seem aware of the power imbalance, but it does not impact their mutual affection for each other, at least not at first; in fact, they both appear to accept the imbalance as a condition of their friendship. Only when someone else, like Mr. Knightley, points out the imbalance, and when Harriet reaches above her lower status, does it feel problematic to Emma.
Emma is well-meaning but patronizing toward Harriet, and at times, Emma appears to feel she is doing Harriet a huge favor by befriending her. Typically, this approach to friendship doesn't promise a positive outcome, and sure enough, tension arises between the two women when Harriet goes above her position to develop feelings for Mr. Knightley. Emma is content to be devoted and affectionate to Harriet, but only as long as Harriet stays in her expected position. These kinds of conditions certainly do not meet the standards of true friendship, but Emma is young and naive. As she matures, she learns what it means to be a true friend to someone else, so the relationship between herself and Harriet inevitably changes.