When they manufacturer paper, how do they actually arrange the direction of the grain in the paper? What is the actual "grain" in short grain vs. long grain? Is all paper either short or long grain or is some "omnidirectional"?

It's noted on most wrappers or boxes what grain it is. Most boxed 8.5x11 and 11x17 is long grain. If you fold a piece of paper vertically and horizontally you'll see one way will fold easier. That's the grain of the paper. 17x11 is short grain. Being some presses feed paper the long way...and some the short way. It's made both ways. When printing 2-4 color it's sometimes more critical on text weight to have the right grain so the image fits in register. Being it's a lighter sheet it will stretch easier making the image fit and register more difficult. It can be a trade off sometimes depending on the bindrey finishing of the job. Cover stocks are a little more forgiving being a heavier sheet. In most cases if the job folds and it's on cover we'll go with the grain to the fold. Otherwise it can crack even if scored sometimes and you'll get those ratty looking edges along the folds. If the cover has a full bleed/solid the cracking will show white in severe cases even if it's scored against the grain. So just remember most stocks can be had in either grain. If not in wrapped ream box stock larger sheets can be had to get the correct grain. So look to the wrapper/box for the grain. In some cases the larger number is the grain of the paper. Ex 8.5x11 grain is going the 11" direction. 11x17 grain is going the 17" direction. When you see the larger number first like 17x11 it will be 11" short grain and so on. This also applies as the sheet gets larger like 12x18, 17x22,, 23x35, 26x40, etc... and so on. If your looking for a specific grain for a job speak with your paper sales rep. They can tell you exactly what you'd need.