Why isn't hearing the same as tasting? How do we feel and differentiate external stimuli?
The problem you are seeking an answer to is referred to as the hard problem of consciousness, the term originally coined by David Chalmers, or more generally the mind-body problem.

Just how "hard" this problem is seems a bit unclear; some people argue it isn't truly "hard" at all, but they make these claims in support of their own particular views of the nature of consciousness. Since not everyone agrees with them, it seems like to at least some extent the "hard problem" description is appropriate.

There certainly are quantum explanations, and you will find proponents like Stuart Hameroff, but most neuroscientists consider his theories to be crank science since he hasn't provided any evidence of his theories, only hand-waving explanations of how they could be plausible.

There are also metaphysical explanations, going back to the dualism of Rene Descartes. The problem with these metaphysical theories is that they aren't scientifically disprovable, and the more we learn about the brain the more of its functions can be explained physically. Dualism is ultimately a religious or philosophical stance rather than a scientific one.

There are several neuroscientific theories of consciousness, including integrated information theory(IIT) and global workspace theory(GWT). For IIT, consciousness occurs through the integration of information in a causal structure like the structure of a brain. GWT proposes that consciousness occurs through the transmission of information through particular central brain structures. In both, the qualia that are experienced occur through the neural substrates of either the processing or the information carried. Hearing and tasting are different because they involve different groups of neurons and synapses; you don't typically taste a sound because the parts of the brain that process taste are not getting direct auditory information.

However, that doesn't mean that senses are completely disconnected: it is possible to form relationships between senses by association, like how both written and spoken language evoke the same meanings, or how certain colors seem to be associated with "hot" versus "cold" temperature.

As far as what it means to experience things how others do, I'd recommend Nagel's What Is It Like To Be a Bat? which argues that subjective aspects of consciousness cannot be completely understood, but that there are objective features that can be understood. So, although you cannot know that others taste or feel music in subjectively the same way as you, you can objectively understand that other people can taste sweet and sour, can hear music in a similar frequency range, etc.