To say "The Son and the Father are of the same substance" (consubstantialem as the word is in the Latin Niceno-Constantinopolitan Creed) is to say that they have the same being (ousia in Greek); that is, that they are the same kind of thing—God.
Traditionally, Catholic theology has said that even though the Son and the Father are of the same substance (consubstantiales in Latin; a semi-reasonable translation of the Greek homoousioi), the Son proceeds from the Father. Thomas Aquinas uses the simile of a word or a thought, which is part of a person (in that thoughts are part of one's mind), but is also in a sense distinct from, and "comes from", one's mind.
Procession, therefore, ... is to be understood by way of an intelligible emanation, for example, of the intelligible word which proceeds from the speaker, yet remains in him. In that sense the Catholic Faith understands procession as existing in God. ... it is clear that the more a thing is understood, the more closely is the intellectual conception joined and united to the intelligent agent; since the intellect by the very act of understanding is made one with the object understood. Thus, as the divine intelligence is the very supreme perfection of God, the divine Word is of necessity perfectly one with the source whence He proceeds, without any kind of diversity.
(Summa Theologica, First Part, Question 27, Article 1)