A citrus juicer is a device designed to extract juice from citrus fruit. There are manually-powered ones, and electric ones. Before choosing an electric citrus juicer, inquire what clean-up involves, and what storage space is required.
A lime squeezer (aka citrus press) is a squeeze mechanism that you work in one hand by pressing firmly in on two handles. You place half a lime in the squeezer end, which has drain ends in it for the juice to flow out, while holding seeds and pulp back.