A total order / linear order is a strongly connected partial order.
A strict total order / strict linear order is a connected strict partial order.
$\preceq$ is a total order if and only if $\prec$ is a strict total order.
A total order / linear order is a strongly connected partial order.
A strict total order / strict linear order is a connected strict partial order.
$\preceq$ is a total order if and only if $\prec$ is a strict total order.