Gasp I think I am a grognard now
My guess is that some grognards would take issue with your definition, or at least the OSR grognards that feel D&D changed for the worse with Dragonlance and was only revived with Labyrinth Lord et al.
But what is a "grognard," really? It is yet another term that is used differently, depending upon who is using it. The classic definition is much more narrow and refers to a wargamer who is probably old enough to remember life before D&D and adopted it as a secondary pursuit to wargaming. So we're talking about folks born in the early 60s or earlier.
A looser definition is someone who plays, or at least
prefers, older versions of D&D, even following a formula of "the older the better." It seems that "Old School" and grognards have some overlap but don't mean the same thing. As I implied above, Old School seems to refer to D&D pre-Dragonlance, or pre-metaplot (maybe pre-THAC0?), whereas grognard is specific to wargaming roots
and/or preference for an older version of D&D other than the present one. In other words, one could loosely use the term and say they are a "3E grognard" but they couldn't really say they are into "Old School 3E."
To put it another way, "grognard" is more of a relative term than Old School, which is more fixed and refers to a specific era of D&D with a distinct beginning (1974) but a variable end-date (usually between 1977 and 1983, although some move it up to 1989, and then there are the OSR games that harken back to pre-83 gaming).