Line simplification is one normally done using Douglas-Peucker algorithm such as with v.generalize tool in GRASS.
I would say they are not the same thing.
A pseudo node is a network "thing", a junction with a valency of two, i.e. 2 polylines connecting to a single point. So if you dissolved these two lines to remove the pseudo node then you get a single line that looks the same.
Line simplification, using the Douglas-Peucker algorithm alters the underlying geometry of a line by removing vertices from within the line to simplify the shape of it. My experience is you typically run this on a line by line basis.
So you could have a scenario where two lines are participating in a NETWORK, they connect at their end nodes to create a pseudo node (valency 2) and you could run a line simplification on these to simplify the line but this won't remove the junction, pseudo node. To do that you want to dissolve the lines.