Consider the angelkin aasimar. If I make an angelkin character which ability score bonuses do I get? The normal aasimar ones, the angelkin ones, or both? What about the other abilities listed?
You get the bonuses from the variant, plus the Aasimar ones that are not replaced.
In the intro of "Variant Aasimar Heritages": (emphasis mine)
Players may choose one of the following six heritages for their aasimar characters in place of the traditional aasimar racial features. Each heritage presents new ability modifiers, spell-like abilities, and skill modifiers that replace the default aasimar racial traits, as well as a pair of custom traits. Each entry also discusses the most common (though by no means ubiquitous) personality traits, physical features, and places of origin of aasimars with that particular heritage.
So you keep everything from Aasimar except ability modifiers, spell-like ability and skill modifiers. For those you take the ones from Angelkin.