Arcana: A character's Arcana is determined by two major factors, that being the facade the character portrays and their personality. As an example, a man who leads a corporation who exudes confidence, while struggling in convincing himself that he's surpassed his father would most likely be of the Emperor Arcana as it's a card that deals with control, leadership and issues relating to the father.

In general I use a combination of keywords and the arc your character goes through to guess at what Arcana your character would be, but how accurate this is depends on my familiarity with the canon and your character's motivations and struggles.

Social Link: A Social Link can be thought of as a bond between the Fool and the other Arcanas developed as he/she goes through the stages of life in order to achieve completion (World). As such a Social Link is not necessarily the same as the character's Arcana, due to Social Links being related to relationships.

Of note too is that a character so linked typically starts off exhibiting many of the negative traits of their Arcana. This is why the power of the Arcana is said to be set free when the Social Link is maxed, as the Fool has experienced all the facets of the Arcana.