Out at first not a force play

[greymule]

R3, R1, 2 out. BR hits ground ball to F6, who steps on 2B for the third out. Everybody knows that R3's run does not count even if R3 crossed the plate before the out. The third out was a force play.

Same situation, but F6 throws to F3 for the out at 1B. Everybody knows that R3's run does not count even if R3 crossed the plate before the out. The third out was made by the BR before he reached 1B safely.

But why is the BR's out not considered a force out? Can anyone think of a play in which the distinction between the BR out before reaching 1B and a runner being forced out at another base makes any difference? If the BR out before reaching 1B has exactly the same effect as a force play, why do we draw the distinction?