Every character goes on a figurative journey; they begin with a dream or goal, struggle with challenges, reach a crisis, and make a choice. But each character’s journey is unique to them. Some advance faster than others, and many start and end at different times.
Most stories begin with a protagonist who has recently decided on a goal, or is about to think of one, and end when the protagonist resolves their goal, either through success or failure. That leaves three distinct possible relationships between protagonist and antagonist.
The protagonist and antagonist could advance along parallel lines. They both conceive of their goal at the same time, and advance at roughly the same pace. These stories usually involve friends or professional peers, characters who know each other. There may be a friendly rivalry, but nothing serious, yet. Then something changes, pushing both characters into a crisis. One will do anything to achieve their goal, while the other refuses to cross certain lines. Examples include the film The Prestige, or the video game Kingdom Hearts.
The antagonist could be one step ahead; working through challenges when they cross paths with the protagonist. It could be chance, or the protagonist could be in the way; in either case, the encounter leaves the protagonist with a new goal, or a new opportunity/threat to their goal. Aladdin is a strong example; Jafar is already close to achieving his goal when the story begins.
The antagonist may have already resolved their journey; achieving a new status quo either through success or failure. Often the antagonist is in a position of power, preventing the hero from achieving their goal. Examples include various tyrants who rule unjustly, until one among the people rise up to become the protagonist, whose goal is to overthrow the antagonist.
Keep in mind that every character perceives themselves to be the hero of their own story. Even the antagonist justifies their actions through some twisted logic. Common reasons include “for the greater good”, “I deserve this”, “I practice a different moral code”, or “I don’t believe in morality”. Whatever the reason may be, understanding how and why a character thinks and perceives themselves is crucial to making the character feel real.