Dpkg and RPM provide a mechanism called triggers. But are they doing the same thing?
There are two different types of triggers for Dpkg: explicit and
file. In the case of explicit triggers, the script of a package A will
activate a package B. The file type is more frequently used. In that
case, the creation, modification or deletion of a file in a path declared by
a package B will activate the package B. The triggers are often used when
a package A has to register an information to a package B. For instance,
when a graphical application is installed, its package will add its
description in the
/usr/share/applications directory, which will trigger
desktop-file-utils package, which will do what is necessary to add a
new menu entry in the window manager.
RPM's triggers function differently. The installation, update or removal of a package A will activate a package B if this package B declares its interest for the package A in its SPEC file (with possible restrictions on package A's version). The documentation of RPM and Fedora gives a few examples of use, like the update of symbolic links when one mail server is replaced by another.
Altogether, despite both mechanisms have the same name, they do not have the same goal. In the case of Dpkg, the triggers are especially useful to group similar actions. For instance, to update the list of manual pages once after installing a hundred of packages, instead of a hundred of times, after installing each package. They are also useful to transfer commands from a large number of packages to a central one, thus easing the evolution of the system. In the case of RPM, the triggers seem more specialised, as they always are about the relationship between a pair of packages.