Hari Raya Puasa (A Malay term confusion)

Why hasn't anyone addressed this issue of lingo confusion: In Malaysia and Singapore, the Malay people call the day that begins the month of Syawal in the Islamic Hijrah Calendar as "Hari Raya Puasa" instead of "Idul Fitri" or related pronunciations...

As "Hari Raya Puasa" literally means "Fasting Celebration Day", it would be a blatant oddity as Muslims are forbidden to fast on the date of 1 Syawal! And while their Indonesian counterparts say "Selamat Lebaran" to each other, the Malays a say "Selamat Hari Raya", which is damn weird considering that the term "Selamat Hari Raya" means "Happy Celebration Day". Thus, the greeting "Selamat Hari Raya" should also be applicable to other Celebration Days as well, such as Christmas, Chinese New Year, Vesak, Deepavali, etc.

Can any Malay give a decent answer to this confusion?