[mesmark]

How would you explain the difference between a shortage of something of a lack of something? I can't seem to find a clear pattern.

a lack - is not having the thing/part to complete something

a shortage - is not having enough of something

in both cases of not enough, either can be used but only a "lack of" can be used when you don't have any at all.

but I would say "a lack of sleep" not "a shortage of sleep"
"The student performed badly on the test due to a lack of sleep."