Synonyms don't ALWAYS mean EXACTLY the same thing. It's one of those titchy, quaint little rules of English.
In military terms, a tactical weapon is something that could take out a heavily armored bunker. A strategic weapon is something that takes out the bunker, and the entire city around it.
In WWII, Tactical bombings targeted enemy troops, command posts and facilities to destroy armies, strategic bombings attacked cities and economies to destroy the enemy's ability to replace their armies.
Tactics are quite often how you accomplish a strategy.
In baseball your strategy is how you attack the entire season, managing the roster, lineup, rotation and bullpen so that you get to October not just as a playoff bound team, but in shape to do something about it. That's partly on Theo but Tito definitely plays his role. It was Grady Little's utter inability to do this well that cost him his job here. As a big picture strategist Tito is superb.
Tactics are in-game stuff. Bunts, pinch hitters, pinch runners, defensive replacements, that kind of thing. I think we're too close to Tito to really give him an honest rating of his tactics, since our judgement and the emotions of whether something worked or not will weigh far too heavily into the decision. Also because even the best tactics don't work sometimes and when they don't they can leave the manager looking pretty silly.