When is an image a Portrait when is it a fashion photograph?

It is a Portrait when it focuses on the person's character/personality. It is used to represent power and social status, and most often; class. In the 1900's, rich families (who were the only people available to afford them) would often be painted or photographed the way they wanted. The photographer had no control. The person in front of the lens had 100% control, and the person operating the camera had nothing.

It is a Fashion photograph when it focuses on the clothes rather than the models. They overuse makeup to make the model look more mannequin-like, in order to draw attention to the clothes and to also make the model seem like a statue that only has a purpose to be a 'frame' for the clothes. The model has no control over the camera, the photographer has full control.

To what degree should an image manipulated to go into a fashion magazine?

I believe that an image should be manipulated just enough. For instance, if the model has bad skin, then airbrushing the defects away seems like a good idea. Elongating the neck, and completely reshaping the persons' face and/or figure, is completely unnecessary. That person is no longer 'them', they are a different person.
That being said, if the person felt comfortable with the changes taking place then that is their decision. If they are not comfortable with the changes and wish for it to be published with no physical manipulation, then that is also their decision and should be considered equally as much as the editors decision. People, whether modeling clothes or not, should be able to say how they want people to see them. They should be happy with the final product, and if not, then it shouldn't be published. Fashion magazines take into account the editors decision a lot more often than the models. They give off the vibe that they don't actually care about the models because at the end of the day, the magazine gets paid money for every sale. If it looks good, it sells.

Is there a clash between the creative and commercial side of fashion Photography?

I believe there is a clash between the creative and commercial side of Fashion photography, as there are disagreements in every industry, fashion is one of them. The fashion photographer may feel that something should go into the magazine because of its beauty, creativity and uniqueness. Whereas the editor may feel completely different because the product may not endorse what they are trying to sell, and for that reason, might deny the photograph from being printed in the magazine.
Some people believe that fashion photography isn't 'photography'. They say this because they believe photography tries to engage the viewer getting them to think, whereas fashion photography is just making it look good in order to sell the item and make money in the process.

Photography has changed a lot over the past 90 years.
One example showing this is how Rich and Powerful people had portraits made for them (how they want themselves to look) to the works of Portraiture photographers depicting their inner-conflicts and catching their clients in moments when they are least prepared.
One Portraiture Photographer who is an amazing example of this is Diane Arbus.

Diane Arbus was born on March 14th 1923 in New York, to parents David Nemerov and Gertude Nemerov who owned Russek's (a famous Fifth Avenue Department store.) Due to her family's wealth, Diane was safe from the effects of the Great Depression while growing up in the 1930's. She started a commercial photography business with her husband (Allan Arbus) creatively called "Diane & Allan Arbus" with her as the Art Director and Allan as the photographer.
In 1956, Diane quit the commercial photography business and began photographing for Esquire and The Sunday Times Magazine.
This experience led to her changing her approach to photography, starting to establish a strong personal relationship with her subjects and re-photographing some of them over many years to capture not only physical changes, but emotional changes.

One of her most well-known photographs is of a Child with a Toy Hand-Grenade in Central Park titled with the same name. She is well-known because she used her camera to strip away anything that she didn't want her audience to see, however, this led to major criticism and that she photographed 'freaks'. Which is not how she wanted to be remembered. In 1971, Diane took her own life and led to people wondering if she saw herself in these "freaks" that she was photographing. Was she led by curiosity, or did she want to show her feelings through other people?