Usualy a Daoist are those who try to seek immortality in novels going agaisnt the heavens to increase their power. While Taoist are seen as being who wield magic or are capable of exorcising ghosts and curses they usually lean more towards being monks compared to Daoist who could also be demonic cultivators. at least in many novel I have read it's been like this.
imo it steam from the media translator exposed to~ before wn where dao stuff popular, hongkong movie come first which popularize tao associated with supernatural exorcism, during 80's perhaps? vampire, demon and such stuff~ they also pop up on journey to the west where one of the hurdles wukong against 3 demon taoist priests~ the cinema platform is so used to Tao when it full stuffed with supernatural theme while dao kinda recent with more against the heaven~ hence you may feel on novel and cinema tao is supernatural while dao is typical fantasy while in fact nah~ again it just translator choice like using chi and qi
Hmm, well. The 'Daoist' in your view seems to be cultivators and ascetics that want to ascend to immortality, while 'Taoist' refers to exorcists. (Edit: one of the reasons that might be the difference between these two kinds of Daoists is the existence of different sects/branches/whatevers of Daoism. The first one sounds a little closer to Quanzhen, while the latter sounds more similar to Zhengyi) Honestly this seems more like what @asriu said, a difference in the translation habits of the translators. So if I went on my previous analogy of yogurt, it would be like if I was told that 'yogurt' referred to the liquid kind and 'yoghurt' is the more viscous kind. In reality the two terms mean the same thing. To illustrate my meaning, that game Immortal Taoists obviously features taoists that are more cultivators than exorcists. They could have just as well went with Immortal Daoists, it changes nothing.