No. You can find an online casino that allow you to play casino games on almost any phone but all casinos do not work on all phones.
Mobile casinos that are developed using html5 and that does not require you to download an app can usually be played on most smart phones. Mobile casinos that requires you to download an app usually only work on selected phones. Some casinos only work on Android or iOS but it also common that a casino supports both operating systems through different apps.
Some mobile casinos offer special apps for tablets to be able to optimize the experience on all units.
It is very common that casinos that requires you to download an app only work on the largest platforms. Usually only Android, iOS and maybe Windows mobile. Some of the larger casino also offer apps for smaller platforms.
It is usually very easy to find out if a casino support your phone or not. Simple go to the casino in your phones browser and find out. The casino will normally redirect you to a page that contains information on how to play (if possible) on your phone.