We can't be certain that there were two companies doing this piece.
In my opinion, these are all Reijmyre, but where a label has been washed off, it would be easy to add another label to make it more saleable.
Now I don't want to seem too suspicious, but, nearly all FM Konstglas pieces have a label and are also engraved on the base. So if you take the label off you still have proof that the piece is FM Konstglas. The label can then be used on a nice piece of glass to make it more saleable.
If a seller has already seen one of these birds with an FM Konstglas label, and has one without a label, and an engraved Konstglas piece with a label, how tempting it must be to transfer the label!!
I think this is one way that eBay myths start, however, I have to say that I could be absolutely wrong, and it could be that both companies make very similar birds....especially as they are hot worked hand made glass, and one artist may have moved from one studio to another.