Moving, move triggers, and recalling

A move is instantaneous and nobody can respond to it, but anything it triggers can be responded to. A recall puts a permanent in its base without being a move at all, which is why it triggers nothing and cannot be blocked by "can't move" effects.

Worked example. In your Main Phase you use the Standard Move of Treasure Hunter ("When I move, play a Gold gear token exhausted") to send it from your base to a battlefield. Exhausting it is the cost (rule 144.2). Moving is instantaneous, with no state between locations, and does not use the chain, so your opponent cannot react to the move itself (rule 448.3, rule 448.3.a and rule 448.3.c). The trigger is evaluated after the move, with the Hunter at its destination (rule 383.2.c), and it goes on the chain, where your opponent can respond. If the destination is a battlefield you do not control and is not yet Contested, it becomes Contested and a cleanup follows (rule 452 and rule 455). If an effect had instead recalled the Hunter from that battlefield to base, no Gold would appear: a recall is not a move (rule 458.1).

The Standard Move. Moving is a Limited Action (rule 448), and the Standard Move is the Discretionary Action that every unit has (rule 421.3 and rule 144). It can be done during your Main Phase, but not in a Closed State and not during a showdown or combat (rule 144.1.a, rule 144.1.b and rule 144.1.c). It moves a unit from base to a battlefield or from a battlefield to base. Only Ganking lets a unit's Standard Move go from battlefield to battlefield, while spells and abilities can move units between battlefields too (rule 144.4.a, rule 144.4.b and rule 144.4.c.1). Several units can move at once to the same destination, from different origins, as one action (rule 144.3, rule 144.3.a and rule 144.3.b). A card changing zones, or an attached card moving with its Top-Most Card, is not a move (rule 448.1 and rule 448.2).

After a move. A moving unit's destination becomes Contested if it is an uncontested battlefield not controlled by the unit's controller (rule 452). When a move is complete, a cleanup is performed (rule 455). A combat occurs only when a cleanup occurs with an empty chain (rule 462), so a trigger from the move resolves first. Units with lethal damage are killed in that cleanup (rule 319.5 and rule 323.4), and a staged combat that stops being staged before its steps begin is not resolved (rule 463.2). In games with more than two players, a move that would put a unit where it can't be, such as a battlefield with a combat between two other players, recalls the unit instead (rule 449.2.c and rule 464.1).

Recall. A recall relocates a permanent from anywhere to its base without it being a move (rule 457). It does not trigger abilities that trigger on moves, and it cannot be prevented by effects that restrict or block movement (rule 458.1 and rule 458.3). It does not change the permanent's state: unless the source says otherwise, its damage and statuses stay (rule 460 and rule 460.1). An unattached non-Unit gear at a battlefield is recalled in the next cleanup (rule 459.1).

Common mistakes. "I'll respond to the move": you can only respond to its triggers. "Recall heals and readies": it does neither unless the card says so.