Some 4X, like Paradox games (Stellaris, Europa Universalis, Crusader Kings), Star Ruler, are real-time: time flows constantly, and game can be paused to make orders.
This lets game has very fine event granularity and easily simulate systems. However, while this works fine in single player, in multiplayer this turn type leads to very frustrating gameplay: when one player has to make decisions, other just has to wait, because they don't necessarily have something to be done.
Like in classic board and computer games, players take turns in succession. Example of game that is consecutive turns only is Shadow Empire. This further unevens the decision load and also introduces the initiative problem: other player can possibly react only when the turn is over. However, this order is simplest to implement.
Modern turn-based games often let players take turns simultaneously, like Civilization, Alpha Centauri, and their numerous knockoffs. This usually lets players make decisions all the time and produces uniform, engaging experience. However, in times of conflict this can lead to players issuing clashing orders, and reaction speed or even network latency determines the winner.
Recent Civilization games offer "Hybrid" turns. When players are at peace, they play simultaneously, when war starts, game switches to Consecutive. This solves the order clashing, but the issue of initiative arises again, and turns are made slowly and game alternates between orders and boredom. Also, even in peacetime some decisions might clash, like religious combat in Civilization 6 (really...).
In games with deferred turns, like Dominions or Freeorion, orders are issued simultaneously and processed on server when all players are done. This solves the initiative and scheduling problems. The problem with this mode is that no immediate results can be obtained until the end of turn. This requires careful game design and allows less instant reward for players.