"Summon" isn't a real Magic keyword—it's a relic of the game's earliest days. Old cards printed creatures as "Summon [Creature Type]" in the type line instead of "Creature — [Type]." For example, the original Llanowar Elves read "Summon Elves." The Oracle rules have since updated all these cards to the modern "Creature" template, so functionally there's no difference today.
The common confusion stems from "summoning sickness," which is the actual rule people mean. A creature can't attack or use abilities with the tap symbol unless you've controlled it continuously since your most recent turn began. This applies regardless of how the creature entered—cast, reanimated, or tokened.
In Commander, summoning sickness matters constantly: freshly cast commanders can't immediately attack, and blink or flicker effects reset the clock, delaying mana dorks and attackers a full turn.