These days, almost every casual jacket (or even suit jacket) gets labeled as a blazer. In the States, the blazer has been re-appropriated to mean almost any jacket with pockets, lapels and unmatched pants, when in fact the jacket may not actually be a blazer, but a sport coat.
With this type of disorder brewing, the blazer and the sport coat often get confused, or worse, the terms are used interchangeably. Yes, the blazer is intended for pants that do not match the jacket, but so is the sport coat. By definition, the blazer should have patch pockets and bronze or silver buttons.
So where does the sport coat fit in? Traditionally, the sport coat was designed for the man on the move, literally, a more "sporty' jacket for the sporting gentleman. The sport coat is a more robust look, originally due to the type of fabrics it dawned, such as tweed. Considering its history, the sport coat often carries patterns unlike the solid-color blazer. Another notable difference between the two is that the sport coat uses flap pockets, along with the occasional ticket pocket up top.
Technicalities aside, both the blazer and the sport coat have different personalities and evoke different moods. A true blazer is intended to be a dressier option, intended to set the man apart from the rest. (Read its history here for a more in-depth analysis).
On the other hand, the sport coat is much less formal, especially considering its origins. Nevertheless, both are still more casual than the suit jacket. Yet no matter how casual, both the blazer and sport coat are an essential elements to use when molding personal style. And even more beneficial once you know how to use them.