  In this paper we show how connections and their generalizations on transitive
Lie algebroids are related to the notion of connections in the framework of the
derivation-based noncommutative geometry. In order to compare the two
constructions, we emphasize the algebraic approach of connections on Lie
algebroids, using a suitable differential calculus. Two examples allow this
comparison: on the one hand, the Atiyah Lie algebroid of a principal fiber
bundle and, on the other hand, the space of derivations of the algebra of
endomorphisms of a $SL(n, \mathbb{C})$-vector bundle. Gauge transformations are
also considered in this comparison.
