Casting a spell means to take a card (and sometimes a copy of a card) from the zone that it is in and put it on the stack, pay all necessary costs and wait for it to resolve and affect the game. Cast was initially an informal term and the official phrase was to ‘play a spell.’ Play can still refer to this process, but the keyword action ‘cast’ was added to the official rules to try and help clarify this.

In the past ‘play’ meant casting spells, playing lands, activating abilities as well as referring to the battlefield and to how to continue the game i.e. ‘play with the top cards of your library revealed.’ Adding additional keywords to differentiate these different actions may add complexity, but it make it easier to explain the game clearly and differentiate what each of these things mean.