It depends on who made the portrait and when. In general, a central notion here is "self-fashioning." Early modern portraits represent the physical appearance of the person and additionally how that person may want to be seen. I would put it this way: an early modern portrait is the equivalent of someone taking 100 selfies in the best clothes/make-up, picking the best image and angle, and then photoshopping it.

To bring the point back to your comment on Henry VIII, Hans Holbein's Portrait of Anne of Cleves perhaps was made to flatter her physique in order to convince the King to marry her. The edited volume Henry VIII and the Court: Art, Politics and Performance may be of interest to you Here's a link to a relevant passage.

You're probably referring to later Western portraiture, proper paintings 'n all (of which I know nothing), but I'll add a quick note on ancient Roman portraits. Roman sculptural portraits could be really realistic and honest - common notion is that Roman art copied everything from the Greeks, but that they 'evolved' sculptural art by 'inventing' realism. Lots of ugly, fat, and wrinkly Roman busts out there just like there were ugly, fat, and wrinkly Romans. But portraits, especially those of the imperial family, were also shamelessly modified when it suited the motives of the contractor. Sometimes this just meant idealizing the features of the sitter, but sometimes the whole individualistic appearance could be purposefully obscured and changed. Most obvious example of this is rendering the portraits of emperor's relatives to physically look like the emperor, to invent shared facial features. This worked even across genders and family members that weren't blood relatives; e.g. the empress Livia could be rendered to look like her husband, the emperor Augustus. The motive was to emphasize the unity and strength of the imperial family, and make sure that whatever virtues of the individual were celebrated, they were always linked back to the emperor.