“Old School” means doing things the way people used to do them. It’s a relative term, since what’s Old School depends on what time you’re using as a reference. Depending on when or who you’re talking about, electric typewriters could be newfangled inventions or unbearably old school, practically antique. School also carries a slight connotation that something may be a conscious decision to identify with a like-minded group (as when one refers to “schools” of artists). It’s perfectly objective, in the sense that for whatever you might be talking about, there really are facts about how something was done in the old days, and techniques and approaches that hadn’t been invented back then. If somebody is doing something exactly the same way that it was done in the past, there’s no doubt or confusion in anybody’s mind when you say that they’re adhering to the old school. That’s true whether they’re banging away on a vintage IBM Selectric, or rolling 3d6 “mud dice” in order for their stats.
Where it gets slightly more complicated is when you want to talk about something that isn’t itself strictly Old School, but is in the style of the Old School. Stylistic decisions are not completely subjective, but do depend on picking out and highlighting certain aspects as salient. Here you can get strong disagreement as to whether the aspects being emphasized are essential, or whether crucial aspects are being ignored, but it’s still not the case that anything goes. You can write entire books about what the essential aspects of Impressionism are, and books disagreeing with those books, but it’s not just in the eye of the beholder. A photorealistic painting by Ralph Goings isn’t it. Neither is the Mona Lisa. View From The Dunes with Beach and Piers may be, but Composition with Yellow, Blue, and Red is definitely not.
When it comes to RPGs, because of their relatively short history Old School almost always refers to the period right at the beginning of the hobby. Among a group of brand-new RPG players who’d never played anything except D&D 4e, you could refer to 3rd edition play without irony as Old School, but addressing a wider audience that includes people who were actually there at the start that’s a recipe for confusion; I’d recommend at least including a quick caveat. Similarly, if you’re going to talk about how you’re playing 4e Old School-style, you probably should spell out what you mean and what aspects of Old School you’re picking up on and emphasizing in your play. (For a humorous look at some of the possibly salient points identified with Old School Play, see Amityville Mike’s “Old School Question Finally Answered” chart.)
Does it matter? Only insofar as words and communication matter. “Next phase, New Wave, dance craze, anyways, it’s still Rock’n’Roll to me” nevertheless presupposes there are things that are Rock’n’Roll and things that are not. There is a sense in which Mozart and Metallica are much the same thing…but that sense is pretty limited. It might help you if you’re asking where in the store you’ll find music CDs, but it’s not likely to be much use in trying to decide whether to buy the CD. If someone told you “it’s all just music, man, stop trying to label it with your rigid definitions” you wouldn’t find that particularly helpful advice if you were trying to arrange with your friends to go to a concert. And if they told you that you’re insistence that there was a difference and that you preferred one over the other was somehow wrongheaded or interfering with their enjoyment, and it’s all just feelings anyway, that’s just a round-about way of telling you to shut up.
Disagreements, even strong disagreements, about what are the essential aspects of a style and what aren’t are not evidence of time being wasted. They’re a learning exercise, at least as long as they don’t degenerate into a flame-war. If you keep an open mind you can learn a lot about what’s important to you about a style when you’re discussing it with somebody who thinks you’re dead wrong–more than you ever learn from somebody who shares all your unspoken assumptions. You might even change your mind. If not, you might at least learn to sharpen those aspects that really do turn out to be essential to your appreciation of the style. People who aren’t interested in what makes up a particular style, whether it’s Old School, New Wave, Impressionist, or whatever, are more than welcome not to join in that particular conversation.