Qualitative research is purely a category of research methods, and can be used for a variety of business needs / research goals. Qualitative "qual" research methods are can include observation, ethnography, 1:1 interviews, focus groups, and more. Qual research typically deals with unstructured data like behaviors, audio, text, imagery, videos, etc unlike quantitative research that deals with measureable quantities (i.e. statistics; numbers) like survey data, transactional data, etc.
UX research will likely leverage several qualitiative methods to uncover the underlying motivations, instincts, and preferences along a product purchase cycle (from awareness/discoverability, exploration, intent, conversion, usage, and repeat). For software companies, examples of UX research projects could include exploratory research to understand buyer mental models when making purchases or usability studies to see how users will interact with screens and flows within your product.
At Momentive, we have UX researchers that support both product and marketing teams to ensure we have intuitive, delightful user experiences across our logged-out websites and logged-in product. Product marketing may be involved in a variety of these projects (both as a contributor and as a consumer of the insights).
Other ways I use qualitative research as a product marketer include developing buyer personas, testing messaging or product names, getting feedback on new pricing models / packages, gathering perspectives for thought leadership, getting feedback on a new pitch, and more.