As the comments usually remind us, the smallest feature size varies in interpretation from company to company, and node to node. You cannot assume how Samsung compares with Intel, GlobalFoundries, or TSMC based on the nanometer rating alone, better or worse. In fact, any specific fabrication process, when compared to another one, might be better in some ways yet worse in others.
With all of that in mind, Samsung has announced the progress they've made with 14nm, 10nm, and 7nm fabrication processes. First, they plan to expand 14nm production with 14LPU. I haven't been able to figure out what this specific branding stands for, but I'm guessing it's something like “Low Power Ultra” given that it's an engineering name and those are usually super literal (like the other suffixes).
As for the other suffixes, Samsung begins manufacturing nodes with Low Power Early (LPE). From there, they improve upon their technique, providing higher performance and/or lower power, and call this new process Low Power Plus (LPP). LPC, which I believe stands for something like Low Power Cost, although I haven't seen this acronym officially expanded, removes a few manufacturing steps to make the end product cheaper. LPU is an extension of LPC with higher performance. Add the appropriate acronym as a suffix to the claimed smallest feature size, and you get the name of the node: xxLPX.
14LPU is still a ways out, though. Their second announcement, 10LPU, is expected to be their cost-reduction step for 10nm, which I interpret to mean they are omitting LPC from their 10nm production. You may think this is very soon, given how 10LPE has just started mass production a few weeks ago. Really, this is a quite early announcement in terms of overall 10nm production. The process design kits (PDKs) for both 14LPU and 10LPU, which are used by hardware vendors to design their integrated circuits, won't ship until 2Q17. As such, products will be a while behind that.
To close out, Samsung reiterated that 7nm is planned to use extreme ultraviolet lithography (EUV). They have apparently created a wafer using 7nm EUV, but images do not seem to be provided.
Development kits for 14LPU and 10LPU are expected to ship in the second quarter of 2017.