As far as I have seen, columnaris only attacks fish but its not a fungus. It's a gram negative bacteria. However, in appearance it does closely resemble a fungus. In order to fight it, you need a medication that fights gram negative bacteria like Furan 2, maracyn 2 or kanaplex.
If it is a fungus - that's a lot better news then columnaris! Fungus can be treated fairly easily - just follow the instructions the other members gave. ALso if you can find Quick Cure at walmart, it works wonders on fungus. It's sold as an ICK medication but the malachite green in it will get rid of fungus as well.
I cant post the link because its aganist the rules to link to other fish forums but if you go to ultimatebettas.com and go to betta diseases and then look under the pinned topics, they have a sticky that is about columnaris and fungus with pics and info on how to tell them apart. The sticky is called "It's not always Columnaris".
I used to get something like that growing on my decor but I do not know what it was and it wasn't in long strings like in the last pic. It was like the first pic you posted. It was slimy but the fish in the tank seemed healthy. I just washed it off the decor once a week.