Both of them mean bed and they target the same wiki page.
I mostly see ベッド, so I guess it is the common word for bed. In which case should I use 寝台 ?
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(Note that 寝る doesn't necessarily imply sleeping, but can mean "to lie down".)
寝台 is just what it says: an elevated platform (台) for lying down / sleeping (寝) and usually refers to the "bed"s in couchette/sleeping cars in trains (or buses, ships, etc.).