Glad to hear you are enjoying your move!!
Let me make this simple. All of Memphis is in Shelby County, but not all of Shelby County is Memphis. Shelby County is huge (in most respects) and also most large cities are in several different counties - not so here. Shelby County takes in: Bartlett, Arlington, Coliierville, Germantown, Millington, Lakeland and Memphis.
Each of the cities listed above are their own cities. Shelby County collects (property) taxes from all these and each city has their own city tax base with the exception of Lakeland, which does not charge their residents any city taxes.
Cordova is an area - not a city, within Shelby County. Part of it has already been annexed into the City of Memphis and some parts are call the "unincorporated" area, which means they presently those homeowners are not paying city taxes yet. They will as soon as they are annexed. It is not a matter of "if" just when they become annexed.
Now about Cordova - for many years it was a hot new area, with affordable updated homes. The county only taxes also made it very attractive to homebuyers. When Cordova lost it's appeal to become it's own city, many were upset with the annexation and started looking at areas that were already their own city outside of the Memphis City limits.
Germantown is an old city/township. The price per square footage commands more. So, if we were looking for a home with more modern ammenities, perhaps less than 10 years old under the $200K range - Cordova wins hands down.
I have lived in both areas and quite frankly, I loved both. However, timing is everything and depending on your budget, lifestyle, and savvy buying, both could be an awesome investment. Contact a Realtor (if you don't have one - let me know!) and have them show you how your family can find the right fit.