If the Catholic Church teaches that "from" and "through" are the same, then they must be more confused that I could imagine. Both words according to Webster have very different definitions. "To proceed" in the original Greek means to "to be originated" . How can the Holy Spirit have two sources or originate from two sources?
From the Son" and "through the Son" are different ways to express the true doctrine of the procession of the Holy Spirit. A few Fathers used the formulae interchangeably (e.g., Bishop St. Hilary of Poitiers and Patriarch St. Cyril I of Alexandria). According to the Catechism of the Catholic Church, the Greek formula directly expresses the order according to which the Father and Son are the one principle of the Holy Spirit, and implies Their equality as principle. The Latin formula directly expresses the equality of the Father and Son as principle, and implies the order. The great Byzantine Fathers had no reservations about being in communion with those great Latin Fathers and Doctors who openly and dogmatically professed Filioque. Therefore the formulae are complementary, not contradictory.
Photios thought that Filioque entails that the Holy Spirit proceeds from two principles, but because the Father and Son are one in everything in which they are not distinguished by the opposition of relation and they are not relatively opposed in their being the principle of the Holy Spirit, they are the one principle from which the Holy Spirit proceeds, as St. Thomas Aquinas showed. The term principle of the Holy Spirit is a substantive name, but we do not say there are two principles because even though the Father and the Son are two supposita spirating, they are one form, God. We use principle in an indeterminate sense when we confess that the Father and the Son are the one principle of the Holy Spirit.
On the Incarnation of the Word Against the Arians 9 in PG 26:1000A: "David sings in the psalm 35:10, saying:
with You is the font of Life;'because jointly with the Father the Son is indeed the source of the Holy Spirit."
Moreover, the same Saint says in 362 ,Against the Arians 3:25:24 in PG 26:376A :
Everything the Spirit has, He has from the Word (para tou Logou)
Whatever the Spirit has includes His existence, i.e., it includes His essence and hypostasis. Ergo St. Athanasios explicitly taught that the Father, through and with the Son, communicates consubstantial divinity and thus gives existence to the Holy Spirit, without prejudice to the μοναρχία of the Father.
Archbishop St. Isidore of Seville in 636 says :
"The Holy Spirit is called God because He proceeds from the Father and the Son and has Their essence."
"Spiritus sanctus ideo praedicatur Deus, quia ex Patre Filioque procedit, et substantiam eorum habet"
( 7:3 in PL 82:268A)
The saint adds:
"There is, however, this difference between generation of the Son and the procession of the Spirit, that the Son is begotten of One, but the Spirit proceeds from Both."
"Hoc autem interest inter nascentem Filium et procedentum Spiritum sanctum, quod Filius ex uno nascitur; Spiritus sanctus ex utroque procedit." (PG 82:268C),
This, however, does not imply two principles of the Holy Spirit, according to St. Isidore, who says that the Father and the Son are the one principle of the Holy Spirit, in total conformity with the decree of Florence and the faith if the fathers:
"One thing which is consubstantial with two could not at once proceed from them and be in them, unless the two from which it proceeds were one."
"Non enim res una et duorum consubstantialis poterit simul ab eis procedere et simul inesse, nisi unum fuerit, a quibus procedit."
(The Books of Sentences 1:15:2 in PL 83:568C)