Number of total orderings

Question

Is there a name for the following type of ordering on some set $S$ {$a,b,c$} that includes only $>$ and $=$ for example:

$$a>b>c$$ $$a>b=c$$ $$a=b>c$$ $$a=b=c$$

Is there some name for these orderings?

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I know that all these satisfy a total preorder on $S$, since a preoder on $S$ is simply one in which the elements are ordered by the $\geq$ relation. But is there a name for these particular orderings?

Are my examples all instances of total orderings, since all members are comparable?

Is it okay to call these simply various "orderings" on $S$?

Answer 1

The first one is a linear order of 3 points.
The 2nd and a 3rd are linear orders of 2 points.
The last is an order for a single point set.

Answer 2

You could consider it a total ordering of a multiset. For example, for $a=b>c$, the set $\{a,b,c\}$ can be regarded as a totally ordered multiset with one element appearing twice and the another element appearing once.