Photoshop Elements has a "stripped down" version of Camera Raw. I haven't used Elements since its much earlier PSE 5, but I gather it still has limited capabilities.
Lightroom has the "full" Camera Raw "engine" so more capabilities.
But, before you dash off to grab Lightroom, you should realize that it is a "workflow manager" more than just a Raw processor. This means that right off the bat you will be faced with choices and "tasks" about organizing your images before you get to the Raw processing part.
You may initially decide to ignore these things, and many people do, but later they have a way of "catching up", and then you either just "bite the bullet" or you get frustrated and decide that LR was just a waste of time and money.
So, if you really want to start working with Lightroom, I'd suggest getting one of the Lightroom "primers" and working through it, and doing some online research and studying some of the many LR tutorials and articles that can walk you through the various features. Plus, do yourself a favor and work through the Lightroom Help, both the "module" and a pdf version are available, and it is the only "official" Users Guide, and is in fact very well put together. Walking through Help chaper by chapter will really get you up and running!
If, though, you don't want to take the LR management features "seriously" you may be better served looking elswhere for simple Raw processing. The Canon Raw processing software Digital Photo Professional (DPP) is actually nice software for Raw processing without the "baggage" of Lightroom, and it's simple to process a Raw file in DPP and then to convert and save a tiff to open in the Elements editor for further processing!
Saying that, I have been Lightroom-centered for several years, and if you want the management features really, it is top-of-the-line!