There’s quite a significant difference between hesychastic theology and hesychastic practice. Hesychastic theology essentially involves the distinction of God into unknowable “essence” and manifested “energies”, which is standard Orthodox theology. Hesychastic practice, on the other hand, is a spiritual practice in which one attempts to withdraw themselves from the material world, and to focus all of their inner thoughts on prayer, attempting to pray from the heart rather than the mind, with the end result being an inner stillness, quiet, a peace between soul and God, which is what the word “hesychasm” literally means. The connection between the two occurs when the Hesychast succeeds at his efforts, having the divine energies manifested in him and through him.
Now, that may sound exactly like the concept of theosis, which it is exactly, and which is thus why I would disagree that hesychasm is merely a “spiritual tradition”. Hesychastic theology, hesychastic practice, and theosis are all intimately connected. Theosis is essentially the end result of hesychasm, and hesychasm is essentially the end result of theosis. One must be at peace with God to join in his energies, and one must join in his energies in order to be at peace with God.
The really interesting question, is how this all ties into traditional Catholic theology. In my opinion, as I have stated before, Eastern and Western theologies should complement, not contradict, each other. So an attempt to reconcile the two can and should be made. The interesting point is that, unlike in Catholicism, in the East there is no strict distinction made between meditation and contemplation; the two are viewed as intimately connected, and the end result of one another. This is a belief that I believe is true in Catholicism as well. Take the order of Lectio Divina. First, we prepare ourselves for communion with God by communion with the Logos. Next, we prepare ourselves for interaction with God’s energies through meditation, learning to view them as not merely words on paper but as the actual life-giving spirit of God. Then, we actively invoke and directly address these energies through prayer, having realized what they truly are. And then, we partake in them through contemplation, in a mini-theosis of sorts.
As you might have noticed, all the terminology makes this sound extremely confusing and illogical. That is because in the scholarly-oriented West, precise liturgical terminology for even hypothetical subjects has been greatly developed, whereas in the more mystical and practical oriented East the terminology has been developed based on the experiences themselves, with little distinction made as to what actually defines them. So, in reality, Eastern and Western theology work in perfect harmony with each other: they’re just looking at the same sculpture from two vastly different angles.