Turn Sequence vs Gameplay Loop

D&D 5e expressly mentions a gameplay loop in the "how to play" section of the introduction to its rules, and describes it as:

1. The DM describes the environment.
2. The players describe what they want to do.
3. The DM narrates the results of the adventurers’ actions.

Contrary to this, BECMI describes a "turn sequence", using terminology similar to wargaming. The BECMI books actually use several different turn sequences to describe different activities, but here's an example of the most general one:

ORDER OF EVENTS IN A GAME TURN
1. Wandering Monsters: DM rolls 1d6 (Normally checked every 2 turns)
2. Actions: Caller describes all party actions (movement, listening, searching, etc.)
3. Results: If —
    a. a new area is mapped, the DM describes it.
    b. an encounter occurs, skip to ORDER OF EVENTS IN AN ENCOUNTER.
    c. something is discovered (secret door, item, etc.), the DM announces the results.
    d. no encounter occurs, the game turn ends; return to #1.

OD&D actually has no explanation of its game turn. It refers the player to the Chainmail game for the combat sequence and Outdoor Survival game for wilderness travel, and only discusses special considerations that occur while playing. It only explains how to play through an example. AD&D does the same thing, but doesn't make reference to the previous games.