noun, noun which may take the genitive case particle 'no'
riding together; sharing a ride; fellow passenger
Refers to multiple people riding together in the same vehicle, or a person who shares a ride. Often used in compounds like 乗り合いバス (shared-ride bus) or 乗り合いタクシー (shared taxi).
駅まで乗り合いタクシーを利用した。
I used a shared taxi to the station.
乗り合いの客同士で会話が弾んだ。
The fellow passengers struck up a lively conversation.
noun, noun which may take the genitive case particle 'no'
joint partnership; joint enterprise
A business or undertaking in which two or more parties participate jointly, sharing costs, profits, or responsibilities. Less common than the 'riding together' sense.
このプロジェクトは三社の乗り合いで進められている。
This project is being carried out as a joint partnership of three companies.
相乗り specifically means sharing a ride (carpooling) or piggybacking on an existing plan, while 乗り合い is a broader term for riding together or joint ventures.
Compound of 乗り (nori, 'riding', the continuative form of 乗る) + 合い (ai, 'together', the continuative form of 合う). Literally 'riding together'.