The Laning phase is the period of the game where the players, except for junglers ofc, typically remain in their respective lanes and farm minions to acquire gold or trade with their lane opponents to get kills or lane dominance. This phase usually lasts the first 15 minutes and is followed by the mid-game where teams start to group up to actively take objectives like towers and dragons.
Lane phase is the part or the game (0-15/20 mins) in which each person stays mostly in their lane and tries to hit their power spikes. After lane phase people don’t really stick to their lanes and tend to focus more on team fighting to try get objectives. Hope I helped!