That's exactly how I see it too. Style is how you wear your clothes, how they're put together and what you wear with what. Fashion is the actual clothes you buy, not how you wear them. Tomorrow I'll be wearing blue jeans bought several years ago (nicely cut but faded), tatty old trainers coloured with highlighters to make them more interesting, an old orange hoody that used to belong to my mum and is really a bit too small, and a gorgeous maroon tweed jacket with gold buttons. It works, as far as I'm concerned anyway, but none of the clothes are remotely fashionable.
Then again, style is very individual whereas fashion works the same for everyone. When someone goes into New Look, or whatever the equivalent is in other countries, and buys a new jacket or a dress, what they're buying is the comfort of being dressed how most people their (my) age are dressing. Style only works for the person it's on. I could never wear a suit, I'm too short and squidgy. Same with miniskirts. And yet some people can do just that and look great.
I know a girl who spends a fortune on clothes, and is always wearing designer stuff. She goes mad if anyone gets it mucky or even touches it. And yet she's barely remarkable. The only reason she's noticable is because she has a good bone structure and is strikingly pretty, but her personal style is fairly non-descript. She's an example of where fashion is supressing style. It's possible to have both, and some people do, but I think style is more important and it's definitely longer lasting.