Although many people use the terms interchangeably a blazer isn't the same as a sports jacket. A blazer is still formal although less formal than a suit. It won't go well with jeans and looks best with more formal trousers and shoes.
A sports jacket is less formal and, while some people still wouldn't wear one with jeans, I think they can look great with them. The key is to make sure the level of formality across jacket, trousers, shirt and shoes is broadly in line. So jeans will need to be fairly smart (e.g. plain indigo, not heavy washed) along with some smart but not overly formal shoes (brown brogues tend to go well).
A smart grey or navy blazer (which tends to be smooth worsted wool) will look too formal with jeans. But a grey or brown sports jacket (which has a tougher textured wool or other fabric) will look ok with jeans. Navy might be hard to pull off with jeans unless there is enough contrast between them to avoid it looking too matchy.
All just my opinion obviously.
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