  The principle $ADS$ asserts that every linear order on $\omega$ has an
infinite ascending or descending sequence. This has been studied extensively in
the reverse mathematics literature, beginning with the work of Hirschfeldt and
Shore. We introduce the principle $ADC$, which asserts that linear order has an
infinite ascending or descending chain. The two are easily seen to be
equivalent over the base system $RCA_0$ of second order arithmetic; they are
even computably equivalent. However, we prove that $ADC$ is strictly weaker
than $ADS$ under Weihrauch (uniform) reducibility. In fact, we show that even
the principle $SADS$, which is the restriction of $ADS$ to linear orders of
type $\omega + \omega^*$, is not Weihrauch reducible to $ADC$. In this
connection, we define a more natural stable form of $ADS$ that we call
$General\text-SADS$, which is the restriction of $ADS$ to linear orders of type
$k + \omega$, $\omega + \omega^*$, or $\omega + k$, where $k$ is a finite
number. We define $GeneralSADC$ analogously. We prove that $GeneralSADC$ is not
Weihrauch reducible to $SADS$, and so in particular, each of $SADS$ and $SADC$
is strictly weaker under Weihrauch reducibility than its general version.
Finally, we turn to the principle $CAC$, which asserts that every partial order
on $\omega$ has an infinite chain or antichain. This has two previously studied
stable variants, $SCAC$ and $WSCAC$, which were introduced by Hirschfeldt and
Jockusch, and by Jockusch, Kastermans, Lempp, Lerman, and Solomon,
respectively, and which are known to be equivalent over $RCA_0$. Here, we show
that $SCAC$ is strictly weaker than $WSCAC$ under even computable reducibility.
