Anne's relationship with her mother was never simple. What created tension and discord?

There were certainly a few reasons for the discord and tension between Anne and her mother.
For one, Anne hated the long "dreadful sermons" her mother (Edith) subjected her to whenever she misbehaved. Anne concluded that she much preferred her father's type of anger, as it never lasted more than "five minutes." Of course, Anne's opinion about her parents is a subjective one.
Later in the diary, we learn that the "discussions" between Anne and her mother often resulted in a quarrel between the two. In one particular exchange, Edith insisted that maids should be referred to as "domestic help." For her part, Anne disagreed. The discussion concluded with Anne bursting into tears.

At moments like these I can't stand Mother. It's obvious that I'm a stranger to her; she doesn't even know what I think about the most ordinary things.

The above quote fairly alludes to why there was discord and tension between Anne and her mother. Part of the reason is that Edith tended to criticize her daughter frequently; she never accounted for her daughter's maturity level whenever they had disagreements. Rather than try to understand Anne, Edith often resorted to disparaging statements to win arguments.
Another reason for the discord between Anne and her mother is that both individuals had combative personalities.

Yesterday Mother and I had another run-in and she really kicked up a fuss... I simply can't stand Mother, and I have to force myself not to snap at her all the time, and to stay calm, when I'd rather slap her across the face...

Edith acknowledged this fact during a quarrel with Mrs. van Daan. In the exchange, Edith and Mrs. van Daan disagreed about the latter's "modest and retiring" self-description. For her part, Edith proclaimed that she and Anne were the opposite of "retiring" in temperament.

Your husband, Anne and I, though not exactly the opposite, don't let ourselves be pushed around.

So, the factors I discussed above are probably the main reasons for the discord and tension between Anne and her mother.

It is fair to say that the relationship between Anne and her mother is not particularly close. Anne's diary is full of examples of conflict between them. It is not simply that they get on each other's nerves in such a tense, claustrophobic environment, Anne also does not really have any respect for her mother:

I need my mother to set a good example and be a person I can respect, but in most matters she's an example of what not to do.

Part of the problem is that Anne is very much her father's little girl, and she wants to feel the same kind of loving warmth from Edith that she receives from Otto. Yet, Anne sees her mother as cold and unapproachable. There is clearly a clash of personalities here. Anne is vivacious and full of fun, whereas Edith takes life more seriously. However, this is not surprising when one considers the fraught situation in which the Franks find themselves.
However, Edith never comes across as a bad person; she just has a completely different personality from her daughter. One gets the impression that Anne and Edith could well have worked out their differences had they been given the proper time and space.