  We point out that two classes of deformations of integrable models, developed
completely independently, have deep connections and share the same algebraic
origin. One class includes the $T\bar T$-deformation of 1+1 dimensional
integrable quantum field theory and related solvable irrelevant deformations
proposed recently. The other class is a specific type of long range integrable
deformation of quantum spin chains introduced a decade ago, in the context of
$\mathcal{N} = 4$ super-Yang-Mills theory. We show that the detailed structures
of the two deformations are formally identical and therefore share many
features. Both deformations preserve integrability and lead to non-local
deformed theories, resulting in a change of the corresponding factorized
S-matrices. We also prove a factorisation formula for the expectation value of
the operators which trigger the deformation on the lattice; similar results in
quantum field theory play an essential role in the solvability of such
deformations. We point out that the long range deformation is a natural
counterpart of the $T\bar T$-deformation for integrable spin chains, and argue
that this observation leads to interesting new avenues to explore.
