Let's use the simplest possible definitions.
A graph is a set $(V,E)$ of vertices and edges between those vertices, where an edge is an unordered pair $e=(v_1,v_2)$ of vertices. Thus $(v_1,v_2)=(v_2,v_1)$.
A directed graph is a set $(V,E)$ of vertices and directed edges between those vertices, where a directed edge is an ordered pair $\tilde e=(v_1,v_2)_\mathrm d$ of vertices. I'm using a subscript $\mathrm d$ to indicate the pair is ordered. Thus $(v_1,v_2)_\mathrm d\neq(v_2,v_1)_\mathrm d$.
In these definitions, there is no such thing as a 'partially directed graph' with some edges of each type. If you want a directed graph with some pair of vertices linked in both directions, you just include both $(v_1,v_2)_\mathrm d \;\&\; (v_2,v_1)_\mathrm d$.
An (undirected) path is any sequence of edges $(e_1,e_2,\cdots,e_n)$ connecting vertices continuously, which is invariant under reversal, so $(e_1,e_2,\cdots,e_n) = (e_n,\cdots,e_2,e_1)$. A directed path is the same without the reversal property. Generally you think about directed paths if and only if you're thinking about directed graphs.
A simple path is a path with no repeated vertices.