  Let $(X,T)$ be a topological dynamical system and $n\geq 2$. We say that
$(X,T)$ is $n$-tuplewise IP-sensitive (resp. $n$-tuplewise thickly sensitive)
if there exists a constant $\delta>0$ with the property that for each non-empty
open subset $U$ of $X$, there exist $x_1,x_2,\dotsc,x_n\in U$ such that \[
\Bigl\{k\in\mathbb{N}\colon \min_{1\le i<j\le n}d(T^k x_i,T^k
x_j)>\delta\Bigr\} \] is an IP-set (resp. a thick set).
  We obtain several sufficient and necessary conditions of a dynamical system
to be $n$-tuplewise IP-sensitive or $n$-tuplewise thickly sensitive and show
that any non-trivial weakly mixing system is $n$-tuplewise IP-sensitive for all
$n\geq 2$, while it is $n$-tuplewise thickly sensitive if and only if it has at
least $n$ minimal points. We characterize two kinds of sensitivity by
considering some kind of factor maps. We introduce the opposite side of
pairwise IP-sensitivity and pairwise thick sensitivity, named (almost) pairwise
IP$^*$-equicontinuity and (almost) pairwise syndetic equicontinuity, and obtain
dichotomies results for them. In particular, we show that a minimal system is
distal if and only if it is pairwise IP$^*$-equicontinuous. We show that every
minimal system admits a maximal almost pairwise IP$^*$-equicontinuous factor
and admits a maximal pairwise syndetic equicontinuous factor, and characterize
them by the factor maps to their maximal distal factors.
