Our Gemara on Amud Aleph discusses the number of Mincha sacrifices that a priest would bring if he was simultaneously anointed as a regular priest and a high priest. He would end up bringing three sacrifices: one for his anointing as a regular priest, one for his anointing as a high priest, and one for the daily sacrifice brought by the high priest.
Ohr Sameach (Klei Mikdash 5:17) discusses a lomdishe question: Do we consider a high priest to be a regular priest who also has an additional level? Or do we consider a high priest to be a completely different sort of entity? He brings a proof from our Gemara that clearly he is considered a regular priest who also is a high priest. This is why he has to bring two separate sacrifices for the two separate levels that he has been granted. If, on the other hand, a high priest were a separate entity, then his anointing as high priest would completely replace the other level and require only the sacrifice of the high priest.
Let us consider these two ideas philosophically. On the one hand, most enduring changes happen gradually. As they say, easy come, easy go. This is because the immediate inspiration is harder to last, and deeper roots and motivations need to be established. If a person goes on a diet and exercise regimen, it might be out of fear from their doctor or reaching a new weight that does not fit any of their clothes; that might induce a sudden resolve. Long-term success will depend on factors such as how meaningful eating healthfully and exercise are, how good they feel, and whether their energy or health concretely improves, etc. The internal motivations need to be deepened and developed.
Even when a change appears sudden, it often is just a tipping point that manifests externally but is a buildup of inner pre-contemplation and contemplation.
However, sometimes there is an immediate and dramatic transformation. This is represented in the other idea about the Kohen Gadol being an entirely different entity. This may be similar to one approach of the Degel Machane Ephraim (Vayikra 13) to the symbolism of the broken pieces of the Mincha in Psychology of the Daf blogpost Menachos 75. Sometimes one ascertains the entirety in one fell swoop and brings it together. And this idea exists in other areas of Jewish thought, starting with the verse that describes Shaul’s ascension to kingship (Shmuel I 10:6): “The spirit of GOD will grip you, and you will speak in prophecy along with other prophets; you will become a different person.” Additionally, we have the halachic, but also metaphysical, idea that a convert becomes literally and figuratively like a newborn. In various concrete halachic matters, and in terms of having his ledger of sins wiped clean, he is a new person (compare subjects of Yevamos 48b and 62a).
While what the Kohen actually becomes is a halachic distinction, yes or no, from a mystical perspective, every halachic possibility is valid since it represents a particular channel of Torah thought.
Ordinary growth is incremental, and even if eventually a person is totally transformed, since it is slow, it does not feel like it. After all, over time, every single cell in our bodies will be replaced by other cells, but we never change into a different person via that process. On the other hand, if a person becomes so inspired that they completely change, then they can truly become a different person.
(A machlokes actually represents two different truths, not a wrong or right opinion, since there are many facets to Torah. One example is that in the Gemara Rosh Hashana 33b, there is a three-way safek about what is the “teruah” sound of the shofar. Therefore, we blow the three sounds we hear on Rosh Hashana: shevarim, teruah, and shevarim–teruah. Technically, only one sound is the true teruah, and we blow all three versions to cover our bases. Yet according to the Zohar (III:232a), each sound activates different middos in Hashem, and thus all three sounds are necessary.)