A simplicial complex is a set $V$ called its set of vertices together with a subset $\Sigma_V \subset 2^X$ so that the sets in $\Sigma_V$ cover $X$ and is closed under taking arbitrary subsets i.e if $A \subset B \in \Sigma_V$ then $A \in \Sigma_V$.
A simplicial complex is also a topological space with set of points $V$ and topology $\Sigma$.
For two simplicial complexes with vertex sets $V$ and $W$ call a function of sets $f: V \rightarrow W$ a continuous map if it is continuous w.r.t the topologies $\Sigma_V$ and $\Sigma_W$ and a simplicial map if the image of a set in $\Sigma_V$ is always in $\Sigma_W$.
You can also associate a topological space $\mid V\mid$ to a simplicial complex called the geometric realization of $V$.
Are there any examples of simplicial maps that aren't continuous maps? What about continuous maps that aren't simplicial? Does it matter if we only restrict to finite vertex sets? This question was inspired by
Are the homotopy groups of the space $(V,\Sigma_V)$ equal to the homotopy groups of $\mid V \mid$? Are they weakly equivalent? Homotopy equivalent?
This particular question was inspired by the recent post How many homotopy types do you get from three points?
I can't 100% understand the answer because he talks about simplicial complexes being homeomorphic to the nerve of some poset, which is a simplicial set?