  Let $\mathcal{M}$ be a Banach bimodule over an associative Banach algebra
$\mathcal{A}$, and let $F: \mathcal{A}\to \mathcal{M}$ be a linear mapping.
Three main uses of the term \emph{generalized derivation} are identified in the
available literature, namely,
  ($\checkmark$) $F$ is a generalized derivation of the first type if there
exists a derivation $ d : \mathcal{A}\to \mathcal{M}$ satisfying $F(a b ) =
F(a) b + a d(b)$ for all $a,b\in \mathcal{A}$.
  ($\checkmark$) $F$ is a generalized derivation of the second type if there
exists an element $\xi\in \mathcal{M}^{**}$ satisfying $F(a b ) = F(a) b + a
F(b) - a \xi b$ for all $a,b\in \mathcal{A}$.
  ($\checkmark$) $F$ is a generalized derivation of the third type if there
exist two (non-necessarily linear) mappings $G,H : \mathcal{A}\to \mathcal{M}$
satisfying $F(a b ) = G(a) b + a H(b)$ for all $a,b\in \mathcal{A}$.
  There are examples showing that these three definitions are not, in general,
equivalent. Despite that the first two notions are well studied when
$\mathcal{A}$ is a C$^*$-algebra, it is not known if the three notions are
equivalent under these special assumptions. In this note we prove that every
generalized derivation of the third type whose domain is a C$^*$-algebra is
automatically continuous. We also prove that every (continuous) generalized
derivation of the third type from a C$^*$-algebra $\mathcal{A}$ into a general
Banach $\mathcal{A}$-bimodule is a generalized derivation of the first and
second type. In particular, the three notions coincide in this case. We also
explore the possible notions of generalized Jordan derivations on a
C$^*$-algebra and establish some continuity properties for them.
