That would mean the following (figures hypothetical for benefit of the example) :
England bat first and score 100 losing all their wickets.
Australia bat second and score 400 losing all their wickets.
England bat third and score 253 losing all their wickets.
England therefore only totalled 353. Australia therefore don't need to bat again as their innings total was higher than England's total across 2 innings (by 47 runs).
In ODI cricket, like this world cup, and in your example:
Team A scores 250 losing 6 wickets
Team B scores 252 losing 4 wickets means they win by six wickets as that's how many wickets they had left.
If Team B scored 252 losing 7 wickets, they'd win by three wickets as that's how many they'd had left before being all out.
You win 'by runs' if you bat first and defend your total (restrict the team batting second getting to the total, as follows:
Team A scores 250 (doesn't matter how many wickets lost)
Team B scores 200 by the end of the innings OR losing all their wickets.
Therefore Team A won by 50 runs.