- An actor is "cast" in a role: Jane Lee is cast as "Jo Smith".
- A sculpture is "cast" in bronze: molten bronze is poured into a mould.
- A variable is "cast" as a certain type of information in programming: is
1the number one, or a string consisting of the character
'1'? You "cast" it to resolve that problem.
Are these all the same verb at the root?
Here are the relevant verb definitions from Oxford Dictionaries Online:
1 [usually with adverbial of direction] chiefly literary Throw (something) forcefully in a specified direction: he cast the book down on to the chair angrily the fishermen cast a large net around a school of tuna figurative individuals who do not accept the norms are cast out from the group
4 Shape (metal or other material) by pouring it into a mould while molten: when hammered or cast, bronze could be made into tools
4.2 Arrange and present in a specified form or style: he issued statements cast in tones of reason
[unnumbered, noun] The actors taking part in a play, film, or other production: he draws sensitive performances from his inexperienced cast
Here's a definition from Merriam-Webster Learner's Dictionary for cast as a verb in relation to actors:
4 a : to assign roles for (a play, movie, etc.) to actors. cast a play
b : to assign (an actor or actress) a role in a film, play, etc. She was cast as a college professor who becomes a spy.