I think flat affect and pervasive pattern of detachment from social relationships is the key point.
following is from uptodate
Schizoid — DSM-5 diagnostic criteria for schizoid personality disorder are as follows :
●A. A pervasive pattern of detachment from social relationships and a restricted range of expression of emotions in interpersonal settings, beginning by early adulthood and present in a variety of contexts, as indicated by four (or more) of the following:
•1. Neither desires nor enjoys close relationships, including being part of a family.
•2. Almost always chooses solitary activities.
•3. Has little, if any, interest in having sexual experiences with another person.
•4. Takes pleasure in few, if any, activities.
•5. Lacks close friends or confidants other than first-degree relatives.
•6. Appears indifferent to the praise or criticism of others.
•7. Shows emotional coldness, detachment, or flattened affectivity.
Avoidant — DSM-5 diagnostic criteria for avoidant personality disorder are as follows :
A pervasive pattern of social inhibition, feelings of inadequacy, and hypersensitivity to negative evaluation, beginning by early adulthood and present in a variety of contexts, as indicated by four (or more) of the following:
●1. Avoids occupational activities that involve significant interpersonal contact because of fears of criticism, disapproval, or rejection.
●2. Is unwilling to get involved with people unless certain of being liked.
●3. Shows restraint within intimate relationships because of the fear of being shamed or ridiculed.
●4. Is preoccupied with being criticized or rejected in social situations.
●5. Is inhibited in new interpersonal situations because of feelings of inadequacy.
●6. Views self as socially inept, personally unappealing, or inferior to others.
●7. Is unusually reluctant to take personal risks or to engage in any new activities because they may prove embarrassing.