The following two definitions are from Wiki:
(1)A connected linear algebraic group $G$ over an algebraically closed field is called semisimple if every smooth connected solvable normal subgroup of $G$ is trivial. More generally, a connected linear algebraic group $G$ over an algebraically closed field is called reductive if the largest smooth connected unipotent normal subgroup of $G$ is trivial. This normal subgroup is called the unipotent radical and is denoted $R_{u}(G)$. Source in Wikipedia:
(2)A connected Lie group is called semisimple if its Lie algebra is a semisimple Lie algebra, i.e. a direct sum of simple Lie algebras. It is called reductive if its Lie algebra is a direct sum of simple and trivial (one-dimensional) Lie algebras. Source in Wikipedia:
https://en.m.wikipedia.org/wiki/Semisimple_Lie_algebra#Semisimple_and_reductive_groups
From the definition 2, a reductive group is semisimple, but from the definition 1, a semisimple group is reductive.
I hope my logic is correct, but why are there contradictive definitions about these two notions?