It's all different Links.
Link is the same in OoT and MM but it's his descendant in TP because that takes place 100 years after MM. The OoT Link is long dead at that point and is the Hero's Shade that teaches TP Link his sword techniques.
The timeline splitting is because Zelda sends Link to just before they met so he could have his childhood and use his foreknowledge of the future to stop Ganondorf from getting to the sacred realm.
http://zeldawiki.org/images/7/7c/Tim...e_Historia.jpg