  The aim of this note is to compare several anticyclotomic $p$-adic
$L$-functions for modular forms and $p$-adic families of ordinary modular
forms, which have been defined and studied from different perspectives by
Skinner-Urban, Hida, Perin-Riou, Bertolini-Darmon, Vatsal, Chida-Hsieh,
Longo-Vigni, Castella-Longo and Castella-Kim-Longo. The main result of this
paper is a comparison between the central critical twist of the two-variable
anticyclotomic $p$-adic $L$-function obtained as specialisation of the
three-variable $p$-adic $L$-function of Skinner-Urban and the two-variable
$p$-adic $L$-function introduced by one of the authors on collaboration with
Vigni by means of $p$-adic families of Gross points.
