I'm actually doing research on vulnerable and grandiose narcissism and I'll try to explain the differences (I've been doing this or two years and it's still hard).
Grandiose narcissism was first theorized by Freud and other researchers like Horney. It's what I refer to as the "classic" narcissist, the one that society and media refer to as. Grandiose narcissism is marked by high self-esteem, mental well-being, aggression and hostility to information that contradicts their self-concept, high scores of extraversion in the Big Five Personality Inventory, disturbed object relations, injured sense of self, arrogant, little to no empathy, devaluation of others, entitlement, omnipotence, self-aggrandizing, rebellious, impulsively, highly energetic, experience-seeking, self-confident, and open expressions of grandiosity Bushman, B. J., Baumeister, R. F., Thomaes, S., Ryu, E., Begeer, S., & West, S. G. (2009). Looking Again, and Harder, for a Link Between Low Self-Esteem and Aggression. Journal of Personality, 77(2), 427–446. doi:10.1111/j.1467-6494.2008.00553.x Campbell, W. K., & Miller, J. D. (2011). The Handbook of Narcissism and Narcissistic Personality Disorder. John Wiley & Sons. Falkenbach, D. M., Howe, J. R., & Falki, M. (2013). Using self-esteem to disaggregate psychopathy, narcissism, and aggression. Personality and Individual Differences, 54(7), 815–820. doi:10.1016/j.paid.2012.12.017 Kernis, M. H., Lakey, C. E., & Heppner, W. L. (2008). Secure Versus Fragile High Self-Esteem as a Predictor of Verbal Defensiveness: Converging Findings Across Three Different Markers. Journal of Personality, 76(3), 477–512. doi:10.1111/j.1467-6494.2008.00493.x Rohmann, E., Neumann, E., Herner, M. J., & Bierhoff, H.-W. (2011). Grandiose and Vulnerable Narcissism. European Psychologist, 17(4), 279–290. doi:10.1027/1016-9040/a000100. It has undergone many names in the literature some being: overt narcissism, exhibitionistic narcissism, and malignant narcissism. This form of narcissism is captured by the majority of narcissism inventories: the Narcissism Personality Inventory (NPI) is an example Campbell, W. K., & Miller, J. D. (2011). The Handbook of Narcissism and Narcissistic Personality Disorder. John Wiley & Sons.
Vulnerable narcissism is the opposite of grandiose, to an extent. It has been theorized for awhile, but recently has been distinguished as an alternate for of, or subtype of narcissism Campbell, W. K., & Miller, J. D. (2011). The Handbook of Narcissism and Narcissistic Personality Disorder. John Wiley & Sons. The Five-Factor Narcissism Inventory (FFNI) is the most recent narcissism inventory and the only one that I'm aware that measure both grandiose and vulnerable narcissism. It consists of 10 subscales of grandiose, and 5 subscales of vulnerable and was created using clinician, peer, and stranger evaluations of diagnosed narcissists along with high-scoring questions from many other narcissism inventories, and the Big Five domains of neuroticism and extraversion Glover, N., Miller, J. D., Lynam, D. R., Crego, C., & Widiger, T. A. (2012). The Five-Factor Narcissism Inventory: A Five-Factor Measure of Narcissistic Personality Traits. Journal of Personality Assessment, 94(5), 500–512. doi:10.1080/00223891.2012.670680. Vulnerable narcissism is marked by anxiety, depression, low self-esteem, contingent self-esteem, anxiously searching for validation of others, difficulty expressing anger, loneliness, unconscious feelings of grandeur, hypersensitivity, timidness, and insecurity. To a large extent vulnerable and grandiose narcissism are polar opposites of each other, but both share interpersonal antagonism Campbell, W. K., & Miller, J. D. (2011). The Handbook of Narcissism and Narcissistic Personality Disorder. John Wiley & Sons. Glover, N., Miller, J. D., Lynam, D. R., Crego, C., & Widiger, T. A. (2012). The Five-Factor Narcissism Inventory: A Five-Factor Measure of Narcissistic Personality Traits. Journal of Personality Assessment, 94(5), 500–512. doi:10.1080/00223891.2012.670680 Kernis, M. H., Lakey, C. E., & Heppner, W. L. (2008). Secure Versus Fragile High Self-Esteem as a Predictor of Verbal Defensiveness: Converging Findings Across Three Different Markers. Journal of Personality, 76(3), 477–512. doi:10.1111/j.1467-6494.2008.00493.x Rohmann, E., Neumann, E., Herner, M. J., & Bierhoff, H.-W. (2011). Grandiose and Vulnerable Narcissism. European Psychologist, 17(4), 279–290. doi:10.1027/1016-9040/a000100. In fact, vulnerable narcissism is so opposing to grandiose that some researchers believe it isn't a subtype or manifestation of narcissism, but something more akin to Borderline Personality Disorder. Some researchers have found that vulnerable narcissism correlates more to borderline personality disorder than it does grandiose narcissism with a correlation of .98 Glover, N., Miller, J. D., Lynam, D. R., Crego, C., & Widiger, T. A. (2012). The Five-Factor Narcissism Inventory: A Five-Factor Measure of Narcissistic Personality Traits. Journal of Personality Assessment, 94(5), 500–512. doi:10.1080/00223891.2012.670680.
However, some researchers have stressed the importance that vulnerable and grandiose narcissism are not opposite constructs, but the same construct that is manifested differently. Grandiose is manifested by a more communal view in terms of interpersonal situations and vulnerable is a more agentic sense of interpersonal situations Campbell, W. K., & Miller, J. D. (2011). The Handbook of Narcissism and Narcissistic Personality Disorder. John Wiley & Sons. The researchers stress that vulnerable narcissism not be defined by its difference from or opposing correlates of grandiose narcissism, but in its manifestation of behaviors.
My research (not published) examines self-esteem, contingent self-esteem, implicit self-esteem, peer evaluations of self-esteem, self-esteem stability, contingencies of self-worth, social desirability, peer victimization, social groups, and the self-categorization and social identity theories to find a distinguishing factor between vulnerable and grandiose narcissism. I may have bitten off more than I can chew being and undergraduate and it's certain my faculty mentor believes I have. I gave a 30 page questionnaire consisting of over 500 questions with 25-30 subscales to a sample of 110. I'm currently in the process of scoring all the data, by hand. I'm at 50 so I can share some results if people are interested and I may present my research at the BigSURS conference in Asheville this year.
If you have any other questions feel free to PM me. I found the Handbook of Narcissism ( Campbell, W. K., & Miller, J. D. (2011). The Handbook of Narcissism and Narcissistic Personality Disorder. John Wiley & Sons.) to be an excellent resource from an entry level of understanding of narcissism. If you're unable to find it I can email you a copy.
To answer your question.
Grandiose: easily handles rejection, but not isolation. It's hard to say if their ego or self-worth is tied to their self-perception in terms of viewing everything they do as positive or if it is a sort of delusion that everything they do is positive. Extraversion (defined by the Big Five personality characteristic) is dominant.
Vulnerable: does not handle rejection well, but can remain or arguably thrives in isolation. Ego and self-worth is contingent upon the approval or acceptance of others. Introverted, because they score opposite to grandiose in the Big Five measure of extraversion. However, to my knowledge is has not been identified if vulnerable narcissists are introverted primarily whereas it has been shown that grandiose are primarily extraverted. Because vulnerable narcissists score oppositely of grandiose in measures of extraversion they could either be introverted or lack extraversion.