In Galatians 2:9 there is a reference to a handshake between Paul and other Apostles:
So, James, Cephas and John, these leaders, these pillars, shook hands with Barnabas and me as a sign of partnership: we were to go to the pagans and they to the circumcised.
On this respect, the Nova Vulgata reads:
Iacóbus et Cephas et Ioánnes, qui videbántur colúmnæ esse, déxteras dedérunt mihi et Bárnabæ communiónis, ut nos in gentes, ipsi autem in circumcisiónem;
(texts are taken from here)
So, they are not equivalent. The English one expresses the type of act, with the Latin expressing the way the act is performed. The latter is more akin to the Spanish case, where a handshake (apretón de manos) is also said dar la mano (dare manum). Is there a more general way to describe a handshake in Latin than that of the action performed?