Patching SQL Server 2014 Versus SQL Server 2014 Express
Are service packs for SQL 2014 different than the service packs for
  SQL 2014 Express?


There is no difference in service packs or cumulative updates between SQL Server Express edition and other editions such as developer, standard or enterprise.

When looking at the latest build of sql server 2014, SP3 CU4 is the last one with build number: 12.0.6329.1 (Latest build). I'm not sure where SP4 is coming from?

When looking at the applies to field from SP3 CU4: 


  Applies to: SQL Server 2014 Developer SQL Server 2014 Enterprise SQL
  Server 2014 Enterprise Core SQL Server 2014 Standard SQL Server 2014
  Business Intelligence SQL Server 2014 Express SQL Server 2014 Web


You will find SQL Server 2014 Express

Download SP3 CU4 here 

Remember that you would have to apply the service pack first, and then add the CU.
A list of sql server (2014) build versions can be found here, here and an overview of all the recent updates here . 



EDIT


  ...I get the impression that I need to update to SP3
  1st THEN apply the CU4 patch. Since I'm starting with the base version
  of SQL Express (SP1 or SP2 not applied), can I just skip right to
  installing SP3 and then CU4 or do I first need to apply SP1 and SP2?


Since Service packs are cumulative you can directly install SP3 while skipping SP1 and SP2 and then install CU4.


  Also If I were to download SP3, I have a number of choices of files to
  download. Not sure which to pick. See options from this link:
  microsoft.com/en-us/download/details.aspx?id=57473 Appreciate any
  additional guidance you can provide...


The link provided is to download sql server express / local db / express with tools / express advanced edition with the SP3 installed when you don't have express installed.

You should download the regular SP3 patch, without express.

If you follow this link, you will see these two options:



Click on the one without express, SQL Server 2014 SP3

The ones with express are complete instances of sql server with the patch added.

Just to show you that I am not making this up, when scrolling down on the patch notes of SP3, go to the part: "Select the correct file to download and install"



Only install this one if you have no 64-bit version of SQL Server 2014 Express.

And for the correct file: (I think SP2 is a mistake, supposed to be SP3)



A patch for any Edition, express included. The Service pack you need, SP3 is this one .

Afterwards, download and install CU4  for SP3 from here