Turf War - 3 minute timer, whichever team has more ink at the end wins. This mode is only played in casual unranked, ranked is all objective modes. During Splatfests, there's a special 2v2v4 variant called Tricolor Turf War.

Splat Zones - Standard King of the Hill. Ink the point to capture it (some maps have two points, you must control both at once). While your team is in control, your timer ticks down. Whoever hits zero first, or whoever has more progress after 5 minutes, wins.

Tower Control - Payload variant. Tower starts in the center, get on it to ride it along a track towards a goal in the opponent's base. Ride all the way to the goal for a knockout victory, or after five minutes whoever has come closest to the goal wins.

Rainmaker - Reverse capture-the-flag. The Rainmaker is a special weapon that starts in the center of the map and has a barrier surrounding it, pop the barrier to explode ink nearby (and take out opponents that are too close, it's a tug-of-war battle to control pop). Pick it up, and it replaces your normal weapon with a slow charge shot and reduces your movement speed, so teammates need to escort you to a goal in the opponent's base. Reach the goal for KO, or whoever has come closest after five minutes.

Clam Blitz - Complicated. Clams spawn around the map, pick up 8 of them to form a Power Clam. Toss a Power Clam into a basket in the opposing team's base to score 20 points, which also marks the basket as open so that single clams can be tossed in for 3 points each until it closes. 100 points to KO, or best score after five minutes.

https://splatoonwiki.org/wiki/Mode#Online_games