I've never really used PSE, so I can't comment on the different versions of that one or what the adjustment curve might be in transitioning to full Photoshop.
CS stands for Creative Suite, which is what all of the Adobe full professional level programs were in the most recent years before they went to the subscription based model. I am using Photoshop from Creative Suite 6 (aka PS CS6), which is the last creative suite version.
Now the professional ones are all subscription-based. This is called "Creative Cloud" (CC). You pay a monthly subscription and always have access to the latest features, instead of waiting to upgrade once you decide there are enough features to make it worth the cost.
The most inexpensive CC subscription includes Photoshop and Lightroom and is $10/month. For a cost comparison, I paid over $200 just to UPGRADE my Photoshop from CS4 to CS6 in 2012, so for the full version, it's a very good deal. It looks like PSE 14 is still the buy-and-install model you're used to and it's selling for about $70, so if you are happy with the functionality there and tend not to upgrade often, that will be a bit less overall.