In modern O gauge there are basically 2 scales
Standard O (Lionel) or sometimes called full scale O (Williams by Bachmann, and others)
Traditional O (Lionel) sometimes called semi-scale O (Williams by Bachmann, and others)
O27 refers to Traditional scale locomotives and rolling stock that were designed to be used with Lionel's old tubular O27 track. It will run on Lionel's new Fastrack or any modern 3 rail O gauge track. These are usually low cost because they were designed for the toy train market. I really like some of these cars!
O31, O36. O48, O60, O72 & O84 are the curves available for Lionel Fastrack. O31 makes a 31" circle measured from the Center rail, O36 a 36" circle measured from the center rail and so on...
O42 could refer to the minimum curve a locomotive or rolling stock could operate on.
All Locomotives and rolling stock are rated for minimum curve very similar to HO and other scales.
Standard O has become the high end, usually very detailed. Standard O is larger then Traditional O
Traditional O is what most Lionel Christmas trains and other Ready to run sets come in. Most modern traditional O is rated at O31 and most ready to run sets come with O36 track.
Standard O was first introduced by Lionel in the 1970s and is more true to 1:48 scale. Before the introduction of Standard O all Lionel and many other O gauge manufactures trains were what we now call Traditional O hence the name, Traditional O.