The Smritis talk about only two types of Brahmacharis viz:- Naishthika and Upakurvanaka.
Naishthika is one who remains in the studentship phase of life (the Brahmacharya Ashrama) for the entire life. He lives with the Guru (serves the fire in the Guru's absence) and he does not have marriage and the life of a householder.
Upakurvanaka will marry after completing his Brahmacharya Ashrama unlike the Naishtika.
These are the basic differences between the two types of Brahmacharis as mentioned in the Smritis.
Two classes of Brahmacharin have been mentioned by the wise in the
Smriti. The first is Upakurvanaka (a Brahmana, in a state of pupilage,
who wishes to pass on to the state of a householder); the second is
Naishthika (one who leads a life of perpetual celibacy). (8)
Daksha Smriti 1.8
The ritualistic (Naishtkika) Brahmacharin who practises this vow from
his Upanayana (investure with the holy thread) till death, attains to
The twice-born one, who practises this vow for thirty-six years, is
called a Upakurvanak. At the close of this Vrata, the vowist should
shave bis head. Thus having finished the study of all the Vedas or of
any part thereof, he (the student) should give honorarium to his
preceptor (Dakshina) after having obtained his permission thereto, and
bathe thereafter (41)
Vyasa Smriti 1.40,41
And, to my knowledge, these are the only two types that are mentioned in scriptures.
Note that here Brahmachari refers to a person who is living in the first order (among the four orders found in Hinduism) of life.