Every out in a game results in one "putout" for fielding purposes. As I said above, the only difference is that the first baseman gets credit for the putout on this play rather than the catcher, who gets an assist instead of a putout.
The pitcher recieves credit for a strikeout in either case, but strikeouts are not a fielding stat, they're a pitching stat.
Now, if the runner is safe it first, the pitcher still receives credit for a strikeout, but since the runner was safe, there is no putout recorded. And the pitcher will be charged with a wild pitch, or the catcher with a passed ball.
But it's really erroneous to say that when that happens there were "four outs" recorded in the inning.
Since there was no putout recorded when the batter reaches first safely after a strikeout, there will still be only three outs recorded for the inning.
