Says Turrettin, III. xxix. 21. "The Father does not generate the Son either as previously existing, for in this case there would be no need of generation; nor yet as not yet existing, for in this case the Son would not be eternal; but as co-existing; because he is from eternity in the God-head."
As Turrettin says, "The Father and Son spirate the Spirit, not as two different essences in each of which resides a spirative energy, but as two personal subsistences of one essence, who concur in one act of aspiration." Institutio III. xxxi. 6.
Turrettin distinguishes the difference by the following particulars: 1. In respect to the source. Generation is from the Father alone; procession is from Father and Son. 2. In respect to effects. Generation yields not only personality, but resemblance. The Son is the "image" of the Father; but the Spirit is not the image of the Father and Son. Generation is accompanied with the power to communicate the essence; procession is not. 3. In respect to order of relationship. Generation is second, procession is third. In the order of nature, not of time (for both generation and procession are eternal, therefore simultaneous), procession is after generation. Institutio III. xxxi. 3.
Both translations as well as the gloss apparently by W.G.T. Shedd.
(source - see footnotes 2 and 4)
Thus Turrettin: They differ, "1st. As to source. The Son emanates from the Father only, but the Spirit from the Father and the Son at the same time. 2d. As to mode. The Son emanates in the way of generation, which affects not only personality, but similitude, on account of which the Son is called the image of the Father, and in consequence of which he receives the property of communicating the same essence to another person; but the Spirit by the way of spiration, which affects only personality, and in consequence of which the person who proceeds does not receive the property of communicating the same essence to another person. 3d. As to order. The Son is second person, and the Spirit third, and though both are eternal, without beginning or succession, yet, in our mode of conception, generation precedes procession."
"The schoolmen vainly attempted to found a distinction between generation and spiration, upon the different operations of the divine intellect and the divine will. They say the Son was generated per modum intellectus, whence he is called the Word of God; the Spirit proceeds per modum voluntatis, whence he is called Love."
(Vol. I, l. 3, q. 31.) (source - A.A. Hodge, Outlines of Theology, p. 158)