Tanwin comes in 3 flavors: -an -un and -in
Only Tanwin with A (-an) gets an Alif for reasons related to possibilities of reading such words with "A" only when they come at the end of the word. This is something related poetry and eloquence of speech so it is a bit out of the scope here.
However, it is Alif. The short Alif or stroke is really not used in our daily life when writing. This is usually used on letters that have long vowels which are not written in the word, e.g. هذا (háthá) .. a stroke would be placed over "H" to guide readers that there is a long vowel but not written. It is used specifically for learners and new comers to Arabic. In Quran, which has a different orthography system than the standard Arabic, this stroke is used a lot on words to guide the sound and pronunciation properly. Otherwise, we dont really use it in our daily writing