How does the nuclear membrane differ from the cell membrane?

They serve different purposes, but are generally the same thing just on a different scale.

Nuclear membrane is used mainly for protection and transportation of genetic material from one side to another ( one example would be when mRNA leaves it for the ribosomes during protein synthesis).It also has specialized transport cavities named "pores" on which material can trespass.

Meanwhile the in the there are a lot of more chemicals trying to get inside of the cell, being the cause for the abundance of more specialized transport attached to it, causing processes such as facilitated transport and .

It's also important to note that both of them are phospholipid bilayers and are key parts of their structure, in both of them and transport processes occur.