“Faucet” and “tap” name the same kind of water-control fitting in their shared plumbing sense. “Faucet” is the usual US term and “tap” the usual UK term.
“Flyover” and “overpass” are regional equivalents when they mean a bridge carrying one route over another. “Flyover” also has a separate aircraft-event sense, especially in American English.
“Kerosene” and “paraffin” overlap as regional names for a petroleum liquid fuel used for heating and lighting. The match is sense-specific because “paraffin” also refers to wax.
“Movie theater” and “cinema” overlap when they name a venue where people pay to watch films. Cambridge marks “movie theater” as US with UK “cinema,” while “cinema” also extends to films and filmmaking more generally, so the regional equivalence is limited to the venue sense.