Which is the cheaper of the two?
is it correct or it should be
Which is the cheapest of the two?
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Cheaper is a comparative adjective, whereas cheapest is a superlative adjective. (From the google definitions).
As you've already ascertained, they both essentially mean the same thing:
low in price, in relation to similar items or services.
A superlative adjective is an adjective in the extreme comparison. Superlative adjectives allow the writer to take the comparison of nouns to the highest or lowest limits of the quality being compared. As @Anton already mentioned, these are strictly meant for 3 or more nouns (although this is often not followed rigorously).
A comparative adjective is used to compare differences between the two objects it modifies.