topsep, itemsep, partopsep, parsep - what do they each mean (and what about the bottom)?

Ok since you've asked the question with a picture, I'll answer with one (more or less).

Summmary

• itemsep = vertical space added after each item in the list.
• parsep = vertical space added after each paragraph in the list.
• topsep = vertical space added above and below the list.
• partopsep = vertical space added above and below the list, but only if the list starts a new paragraph.

Sample document

documentclass[]{article}
usepackage[margin=1in]{geometry}
parindent=0pt
usepackage{enumitem}
usepackage{fancyvrb}
DefineShortVerb{|}
newcommand{longline}{This is a line of text that will form a paragraph which we can use in various places.par}
newcommand{printvalues}{topsep=thetopsep; itemsep=theitemsep; parsep=theparsep; partopsep=thepartopsep}
begin{document}
hrulefill
begin{enumerate}[topsep=0pt,itemsep=0pt,parsep=0pt,partopsep=0pt]
itemprintvalues
item With all |*sep| values set to 0pt there is no space above or below the enumeration nor between the items or paragraphs within the items.
itemlongline
end{enumerate}
hrulefillpar
hrulefill
begin{enumerate}[topsep=0pt,itemsep=20pt,parsep=0pt,partopsep=0pt]
itemprintvalues
item When we set |itemsep| then this much space is placed between items but no space between paragraphs within an item.
itemlonglinelongline
end{enumerate}
hrulefillpar
hrulefill
begin{enumerate}[topsep=0pt,itemsep=0pt,parsep=20pt,partopsep=0pt]
itemprintvalues
item When we set |parsep| then this much space is placed after  every paragraph within an item.  This will effectively also separate items too, since each single paragraph item will have the |parsep| space after it.
itemlonglinelongline
end{enumerate}
hrulefillpar

hrulefill
begin{enumerate}[topsep=20pt,itemsep=0pt,parsep=0pt,partopsep=0pt]
itemprintvalues
item When we set |topsep| this much space is placed above and below the enumeration. 
end{enumerate}
hrulefill
begin{enumerate}[topsep=0pt,itemsep=0pt,parsep=0pt,partopsep=20pt]
itemprintvalues
item When we set |partopsep| this much space will be placed before and after a list only if the list is preceded by a |par| (i.e., starts a new paragraph)
item This enumerate is not preceded by a |par| so no space is added.
end{enumerate}
hrulefillpar
hrulefillpar
begin{enumerate}[topsep=0pt,itemsep=0pt,parsep=0pt,partopsep=20pt]
itemprintvalues
item When we set |partopsep| this much space will be placed before and after a list only if the list is preceded by a |par| (i.e., starts a new paragraph)
item This enumerate is  preceded by a |par| so space is added.
end{enumerate}
hrulefill
end{document}