When entering a Caught dismissal, the Primary Fielder is the fielder who completes the catch (and is thus credited in Player Averages), while Assistant (Asst) Fielders are any other who have parried the ball during the course of the catch (and are not credited in Player Averages). These fielders will be shown in order on the Scorecard, Scorebook, etc, so the Primary Fielder is listed last.
When entering a Run Out dismissal, the Primary Fielder is the fielder who touches the ball first and does the most to complete the run out, whereas the Assistant (Asst) Fielders are any others who have touched the ball during the course of the run out, including the player who effects the run out by breaking the wicket (most likely the bowler or wicketkeeper). All fielders are credited with a run out in Player Averages, and on the Scorecard, Scorebook, etc, they will be shown in the order they touched the ball: Primary Fielder first, then Assistant Fielder second.
For Stumpings, only a Primary Fielder is allowed, and this will default to the nominated Wicketkeeper (including a replacement wicketkeeper) with Wicketkeeper as Fielding Position as soon as Stumped is selected under Dismissal Type. Obviously, this player will be credited with the stumping in Player Averages.