Skype for Business is not Skype. It's just a rebranding of Lync that happened after Skype acquisition.
There is a half-baked link between Skype and Lync to make it seem like it's the same product. This link is all shitty mainly because Lync and Skype work completely differently, and even simple things like call signaling have to deal with years of legacy Microsoft SIP extensions that were punched into Lync.
I remember the first time we received access to the Lync code repository. That stuff was a multi-GB (!!!) repository that contained files, promo videos, PDFs, code, etc. That tells you much about the development practices behind Lync.
I've the misfortune of being forced to use Skype and I would kill to have it replaced with Teams at my workplace.