Learn Hardcore Russian: Убери швабру в кладовку после уборки, пожалуйста. - Put the mop in the storage closet after cleaning, please.

Убери is the perfective imperative of убрать. It tells someone to do a single, complete action: put it away / remove it (and finish it).

убери швабру = put the mop away (once, to completion)
убирай (imperfective imperative) is more like be putting it away / put it away regularly / start doing it and can sound like focusing on the process or a repeated habit.
убрать is the infinitive, not the normal command form (though infinitives can be used as orders in signs/instructions, but that’s a different style).

Is убрать the same as убирать?

They are an aspect pair:

убрать (perfective) = to remove/put away (result achieved)
убирать (imperfective) = to remove/put away (process, repeated, or general)

In commands, the perfective (убери) often sounds like: Do it once and finish it.

Why does швабру end in -у?