Although it is possible for certain iOS apps (depending on the way they are programmed) to hide the status bar in iPhone and iPad, most of the app (barring games, video streaming apps) choose not to do so.

Safari and Chrome web browsers for iPad have no native control to take browser full screen. While scrolling through the webpage, however, the browser controls and address bar area shrinks to provide a bit more space for content.

While viewing streaming videos however, you do have an option to view it in fullscreen with browser controls hidden. While streaming video, Status bar is shown only when to tap on the screen to momentarily view playback controls.

Safari for iOS

Normal mode

Shrunk controls mode

Chrome for iOS

Normal mode

Shrunk controls mode

Video streaming, full screen mode