I didn't realise they came in different sizes, but screw necked bottles can have a significantly larger inside diameter than corked bottles, and I would always test a stopper inside the bottle neck before I went to the bother of cleaning the bottle or removing the label, sometimes they are too loose a fit or don't touch the sides at all.
With previously corked bottles, these stoppers may need a bit of gentle persuasion to drive all the way home, like a rubber mallet, and some leverage with the back of a knife to get them out again, but they are re-usable and you can store the bottles upright.