I have seen both even in the same context. For example:
May I know the difference and when should one use which?
Chinese Language Stack Exchange is a question and answer site for students, teachers, and linguists wanting to discuss the finer points of the Chinese language. It only takes a minute to sign up.Sign up to join this community
Its prevalence in online media is most likely due to IMEs listing 「台灣」 before 「臺灣」 in Taiwanese phonetic input systems when typing "taiwan" or "ㄊㄞㄨㄢ" on a computer.* This has nothing to do with handwritten simplifications, as things like 「身體」, 「學習」, etc. do not appear as 「身体」 or 「学習」 in Traditional Chinese websites.
Even though one "shouldn't" use the spelling 「台灣」, everyone recognises what 「台灣」 is supposed to be, and this spelling is overwhelmingly prevalent in Taiwan itself, so it doesn't really matter (except when referring to governmental agencies). I would just be cautious in its usage, as the overwhelming (and erroneous) prevalence of 「台」 for the name Taiwan has led people to forget that 「台」 is properly pronounced in the first tone as tāi when used in proper nouns and never as tái.
*This is true from personal experience. Ironically, using a PRC input system set to Traditional Chinese will only list 「臺灣」 and not 「台灣」 when one types "taiwan".
I'm a Taiwanese. '台' is a simplified version of '臺', and they mean exactly the same. NTU's official name is 國立臺灣大學, and we usually call it 台大. It's just a difference between speaking formally or casually. Usually, you'll see "臺"灣 on formal headlines or official documents, because when publishing something serious or when taking an exam, it's preferred to write in strict traditional Chinese.
But in daily conversation and when handwriting, we use a couple simplified words (simply because it's faster and easier) like '台'灣、身'体'、'学"習. The tricky thing is, we only write some particular words in their simplified version, so it's very easy to tell if you're a Traditional Chinese user or a Simplified Chinese user(like people in China)
When typing, we type 99% of words in Traditional Chinese, "台"灣 is a very rare exception. Hope these help.
an old debate lah :)
in 2010, the ministry of education (教育部), of taiwan “declared” that:
all documentations of the ministry, schools, publishers must use “臺灣”. however, other ministries are “informed” (haven’t the authority to force them to follow).
if you can read traditional chinese, read the news here (between the lines, please)
historically, the chinese empire annexed formosa in 1683; most, if not all documentations, used “臺灣”, not “台灣”. eg: in the the official declarations:
if the situation is sensitive, or, formal; stick to “臺灣” 😼