  We introduce the notion of coarse metric. Every coarse metric induces a
coarse structure on the underlying set. Conversely, we observe that all coarse
spaces come from a particular type of coarse metric in a unique way. In the
case when the coarse structure $\mathcal{E}$ on a set $X$ is defined by a
coarse metric that takes values in a meet-complete totally ordered set, we
define the associated Hausdorff coarse metric on the set $\mathcal{P}_0(X)$ of
non-empty subsets of $X$ and show that it induces the Hausdorff coarse
structure on $\mathcal{P}_0(X)$.
  On the other hand, we define the notion of pseudo uniform metric. Each pseudo
uniform metric induces a uniform structure on the underlying space. In the
reverse direction, we show that a uniform structure $\mathcal{U}$ on a set $X$
is induced by a map $d$ from $X\times X$ to a partially ordered set (with no
requirement on $d$) if and only if $\mathcal{U}$ admits a base $\mathcal{B}$
such that $\mathcal{B}\cup \{\bigcap \mathcal{U}\}$ is closed under arbitrary
intersections. In this case, $\mathcal{U}$ is actually defined by a pseudo
uniform metric. We also show that a uniform structures $\mathcal{U}$ comes from
a pseudo uniform metric that takes values in a totally ordered set if and only
if $\mathcal{U}$ admits a totally ordered base.
  Finally, a valuation ring will produce an example of a coarse and pseudo
uniform metric that take values in a totally ordered set.
