There aren't classifications such as a "classical saxohpone" or a "jazz saxophone" for the way a saxophone should be used. But the characteristics of an instrument desired by players in each genre differs a little. A saxophone with a wider taper is generally preferred for jazz because it has a very expressive color. In contrast, a saxophone with a more conservative taper suits classical play because the taper allows for more precise control over intonation. Yamaha puts "Z" in the end of the model name, like the YAS-82Z, to indicate it is well suited for jazz. However, this doesn't mean this model is only used for jazz because musical taste varies from player to player.
When you choose an instrument, choose one which you feel comfortable to play and meets your musical taste.
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