The reason is called 'Bud' and not 'Budweiser' is because there is a Czech town called Budjeovice, or 'Budweis' in German. Be from that town is called 'Budweiser' as in 'from Budweis'.
It's that name Mr Busch used when making a bohemian style lager in the US. Then when the iron curtain fell and the beer from the actual town entered the International market AB InBev made a huge stink, forcing the beer to use a different name in the USA (it's sold as Czechvar).
But then the European Union responded by honoring the 'appellation contrôlé' ruling, where a brand that used a place name is protected, so that only products from that geographical location van use the name.
This is why they have to sell it as bud. But when comparing the beers they should've gone with 'butt'. People know this and don't buy the shitty American stuff. All budget grade beers in Germany are better than it.