That is a question that divides a lot of academics. In simple terms the difference between the two is that:
*Quantitative research is based on the positivist, scientific collection of data, and creation of research projects that strive for objectivity, and reproducability. The idea is that someone else should be able to take your experiment, do it again from scratch, and arrive at the same, or similar, conclusions. The data in quantitative research leans towards the gathering of statistics, and "facts". There are a good many arguements against the thinking behind such research, especially from those who favour qualitative research.
*Qualitative research comes from a different angle, and grew out of ethnographic research- going out into the field and recording subjective and narrative/cultural responses from a sample of people. Here the emphasis is on the sort of data that cannot be contained in statistics- personal, experiential, subjective data.
*As an example, if I were to present a group of people being researched with a multiple choice questionnaire, I could gather statistics on their responses: 56% of readers prefer cats to dogs, and so on. If on the other hand I asked [I]why[I] they prefered cats to dogs, I couldn't represent this data in a graph, but would have a greater depth of response. This is perhaps and oversimplification, but the first would be quantitative research (think Quantity=numbers), the second qualitative (think Quality=experience).
Sorry if that doesn't help at all. With regards to the tape recorder, it would all depend on how you used it. Let me know if you have any more questions, or want some readings recommended.