Monastic life per se is marked by a lifestyle lived in community i.e. with others. The hermit or eremitical life is a life of solitude, lived alone.
Some groups of hermits do live in part a community life. Carmelites, for example, are “hermits in community”. It involves a community life as well as an eremitical type of life of solitude. Some other hermit organizations live in groups and with some degree or other of solitude and aloneness.
The Catholic Catechism mentions specifically those living a strictly eremitical lifestyle alone but without public vows (remaining in the lay state). Public vows is a public consecration to the eremitical life under Canon 603 i.e. consecration by a bishop.
Catholic Catechism: "920Without always professing the three evangelical counsels publicly, hermits "devote their life to the praise of God and salvation of the world through a stricter separation from the world, the silence of solitude and assiduous prayer and penance."460 "
If one makes private vows, often to the evangelical counsels, and thus remains in the lay state, it is not adviseable nor wise to adopt this way of life as one’s vocation without spiritual direction and on an ongoing basis. One is free with private vows to adopt the type of lifestyle “for the sake of The Kingdom” to which one feels called - and again ideally under spiritual direction.
Private vows are covered by Canon Law. Private vows in the celibate lay state by their very nature remains open to a further call from God. One may receive a further call, or one may not. Under Canon Law one can without any sort of dispensation commute one’s private vow or vows to a greater good but not to a lesser good. Canon Law does state who can dispense from private vows and this most commonly one’s parish priest and also one’s bishop. Private vows may be made during Mass with the agreement of the celebrant. Private vows to God are also a very serious matter and never to be made lightly.
One does not have, of necessity, to make any sort of private vow or vows. One can remain in the lay state and simply live a particular way of life “for the sake of The Kingdom”. In this instance also, one may or may not receive a further call from God. One may do this in the lay celibate state - or as a married couple, while the bonds of marriage remain and for life.
It all depends on one’s circumstances provided by Divine Providence and that call and vocation of which one is aware - and again ideally with spiritual diretion on an ongoing basis.
Note: “Private” and “Public” vows are classifications within Canon Law. Even if a person makes a vow or vows during Mass, that vow or vow remains under Canon Law a private vow. The public vow under Canon Law is always consecration by the bishop.