I think that this is right and maybe more simple:
Lets say you have a very good player who is a free agent, you don't want to lose him, but for whatever reason you haven't been able to agree on a long-term deal. You can apply:
exclusive franchise tag: Assigning him this keeps him from talking to anyone at all. He gets a huge 1-year payday (average of top 5 salaries at his position, calculated at the end of the current free agency period, fully guaranteed, or a 20% increase over his last years' salary, whichever is greater)
non-exclusive franchise tag: Assigning him this lets him talk to anyone, but if they sign him then they give you two first round picks. This is a huge price, so it effectively takes him off the market. He gets a huge 1-year payday (average of top 5 salaries at his position, calculated based upon last years' salaries, fully guaranteed, or a 20% increase over his last years' salary, whichever is greater)
transition tag: Assigning him this lets him talk to anyone, and if they sign him then they give you nothing, but you can match their offer. You might also be able to work out a trade-- match the offer, trade him, then get something back. If nobody signs him to a long-term deal, then he gets a decent 1-year payday (average of top 10 salaries at his position, calculated based upon last years' salaries, fully guaranteed, or a 20% increase over his last years' salary, whichever is greater)