The difference may be caused by different recording techniques. Pop, rock, jazz, etc. are usually recorded with the close mic (microphone) technique where instruments are acoustically separated from one another and microphones are placed close to the amp for an electric guitar or close to the strings of a piano. Every piece of a drum kit has its own mic. Electric instruments may even go straight into the mixing board instead of through an amp into a microphone.
This gives a very clear, crisp, detailed recording that may then be even further processed with studio equipment. Most people like this type of recording but some don’t. They say you lose the development of the sound of an instrument as the sound travels through the air, and the blending and natural reverb that occur when a band plays live. Adding artificial reverb to a close miced recording is probably the most common effect used today.
Classical recordings are usually done with a single mic or an array of mics (too much to go into here) capturing the sound of the entire orchestra or the different sections of the orchestra from some distance. They also try to capture the natural reverb of the venue where the recording takes place. So you get a very different sound than you get from a close miced recording. Modern recording techniques are working their way into orchestral recordings and, as someone mentioned, small classical groups may be close miced.
The classical technique tries to capture the sound you would hear at a concert. The close mic technique tries to get a "better" sound than you would hear at a concert, and if you’ve ever attended a rock concert you know why. The sound quality of a rock band playing live is usually atrocious.
This is an oversimplification but gives you an idea of the reasons for the difference in sound.