Most definitely they are not the same. The Greek word for "begetting" (as Kolo demonstrated in one of his posts, using Greek alphabet) is rooted in the word to "generate." Your words are generated, energized, projected reflections of your mind. Because it is a one-way process, it is akin to sonship. The Word does not generate the Wisdom, but rather the Wisdom generates the Word. In the case of God, that generation, like the well and water, is eternal and transcendental. It is true yesterday, today and forever before all times and beyond. So, one can not ascribe a "moment" to the Wisdom generating the Word. It can never be an accomplished or initiated
You are still bound by physical and temporal chains and think of God in human terms. We can only think of God in human terms when we think of Jesus Christ.
OK, so is the difference that in this context "beget" means "to generate" (outside of time), and "proceed from" means "He who already exists is sent"? (I had never heard of the filioque before this thread :)