The Apollo Guidance Computer used core rope memory [1] as ROM and magnetic-core memory as RAM. Both are non-volatile.

The command module did not have a redundant computer or memory, but the lunar module came with a second computer [2] of a different type and running different software.

What you remember is probably the Gemini Guidance Computer's tape drive system, which consisted of three identical tape drives that were connected to the computer through a voter circuity.

[1] https://en.wikipedia.org/wiki/Core_rope_memory

[2] https://en.wikipedia.org/wiki/Apollo_Abort_Guidance_System