Correct, the captain is not a managerial or decision-making leader at levels higher than pure implementation.
The soccer captain might influence who takes the penalty shot, but they don’t choose the lineups, tactics, player recruitment, training workflows, etc.
The “lead” in “team lead” is not referring to leadership in the same sense of this discussion, only in a much narrower implementation-only sense.
The coach is the leader of the team overall. The captain is the player on the field who leads the team on the field. The captain is not the one deciding the strategy for offense and defense; he/she is more responsible for exemplifying character, work ethic, motivating others and keeping up team morale.
The soccer captain might influence who takes the penalty shot, but they don’t choose the lineups, tactics, player recruitment, training workflows, etc.
The “lead” in “team lead” is not referring to leadership in the same sense of this discussion, only in a much narrower implementation-only sense.