The Previous Lubavitcher Rebbe, Rabbi Yosef Yitzchak Schneersohn is said to have divided his chassidim into three groups:[1]
There are Chabad chassidim, chassidim who pray using the siddur constructed by the first Chabad Rebbe, and individuals that are chassidim because of their ancestral ties.
The meaning behind these classifications is as follows: A true Chabad chossid is a person that exemplifies the trait of self-control; their mind is always in control of their impulses. The second individual keeps Chassidic customs, although he is yet to attain a mastery of Chassidic practice. However, the third individual does not at all act like a chossid. Nevertheless, in his blood there are certain Chassidic character traits that are natural to him.
While normative thought would tell us that the third chossid is the lowest, there is indeed some advantage in the third that the other two do not have. For, regarding a person born of Chassidic stock, there are certain positive traits that are ingrained within his very nature.
One must place the above adage in perspective. The Pevious Rebbe said this remark to individuals in America who did not have the outer strappings of chassidim—many were not even remotely religious.
Surely, these individuals had trouble identifying as chassidim. It was to these characters that the Previous Rebbe turned to, telling them not to be dejected, for they too are his chassidim.
[1] Zichron Livney Yisroel Pg. 143.