Regular Battle - 4v4 paint-the-most-area battle. The mode we all know since its reveal. Online only.
Splat Zones - 4v4 mode where teams must conquer and hold one or two specific common areas in the map for 100 seconds. Online only and is the ranked mode in the game.
Battle Dojo - 1v1 local multiplayer only mode where you pop the most balloons in a map.
Single Player - a 27-stage game where you rescue zapfishes to restore the power source of Inkopolis. Plays like a third person shooter adventure game with platforming and painting mechanics of Splatoon.
For all multiplayer modes, the time limit is fixed. As for maps, the game currently has 6 maps for both the regular battle and splat zones. More are promised to come at later dates. Additional modes are also coming plus additional weapons and clothing.
As for being tactical, yes this game is tactical to the core. Just ask the players here.