Yes, there are a couple of words that are used commonly when they actually have technical and more limited meanings and applications. Profession is one of these. (Consecration is another.) The making of private vows does not constitute profession. It is an avowal, a dedication. a significant personal commitment, but it is not a profession. A profession is made publicly and in the hands of a competent authority receiving one's vows; it is an ecclesial act to which one is carefully admitted after mutual discernment. It binds one in law, that is canonically, to new public rights and obligations and thus, establishes the person in a new state of life. Moreover, it gives the People of God the right to certain expectations rooted in this profession. Private commitments, whether using vows or not, do none of these things. Even so, we have begun to qualify profession with the term public (or private) because of how common the mistaken usage (speaking as though profession refers to any vows at all) has become.
But there is a problem in shifting the meaning from an exclusive usage to a qualified one. It happens when we read older texts that simply say "profession" without qualification. JPII, for instance doesn't say "public profession" in Vita Consecrata, but this is what he means when he says "profession". It is what he assumes when he speaks of "consecrated life" or the "consecrated state". He is using the term in the unqualified way it was always used until very recently; in so doing he compares and contrasts a "second consecration" which is an ecclesial act with the consecration of baptism, as well as contrasting profession with vows of poverty, chastity and obedience made by a couple within marriage. In the latter case he is clear these vows do not initiate into the consecrated state. Some may simply not know this and may assume "profession" has the same meaning in recent documents as it did in the past. Bearing all this in mind the bottom line that must be made clear is that whichever usage we adopt (qualifying the term profession or using it exclusively for public commitments) there is a vast difference between private and public commitments.
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*Again, profession is more than the making of a commitment whether one uses vows or other sacred bonds. It includes the Church's calling forth, the person's request to be admitted to public vows, an examination of readiness to make this commitment, the prayer of the whole Church, both militant and triumphant to witness and participate in what is happening here (Litany of Saints) and celebrant's prayer, the making of vows (Profession), the Solemn blessing or Consecration of the Professed (in perpetual profession), the presentation of religious insigniae (ring, cowl, etc.). . . concluding rite with solemn blessing.
As you can see, the rite is an ecclesial act. It involves the entire Church participating in the granting and embracing of a new ecclesial identity with new public rights and obligations. This is where the term public comes from. The commitment is not a private one no matter how hidden the hermit's life. Throughout this rite the Church calls the candidate for profession and the candidate responds. This is repeated in an ongoing dialogue between Church (competent authority) and the one making profession/being professed. It is this entire dialogue of giving and receiving, calling and responding that is referred to as Profession though we refer to the making of vows themselves as profession; this is a synecdoche where one part gives the name to the whole.
Similarly one can speak of one's consecration as a synecdoche where the solemn blessing or consecration names the entire event. When someone refers to this event they will say either "your profession" or "your consecration" but they mean the entire rite and what it occasions canonically, personally, ecclesially, etc. Note well, consecration is not something the professed does with herself; it is something God does to or with her through the mediation of the Church.