Firstly I think that we just have to accept that disciplines can be categorized according to hard or soft and that research can be classified according to pure or applied.
What is the significance of this? A discipline that tends to use quantitative data, tends to be predictive, tends to be experimental is classified as a hard discipline. While a soft discipline is one that tends to use qualitative data, generally no experiments are performed, and no predictions concerning the future are made based on the research performed. As such as biology tends to be quantitative rather than qualitative, the discipline is classified as hard. History f. ex. tends to be qualitative rather than quantitative and thus it can be classified as soft.
However, the world is rarely simple. Some researcher in history may say that, I will argue that my branch of history, or the way I perform history is quantitative and therefore hard science (I don’t know if this would be very likely). And it may perhaps be argued that somebody would classify biology as soft.
With regard to the difference between pure and applied research, this difference is closely tied to the rationale and the purpose of the study as well as the research questions posed. The rationale of applied research would be to use the results for some specific purpose, often related to management related issues.
As the pure and applied classification refers to research, that would theoretically mean that most disciplines could have research that was applied. Though for some disciplines it may be difficult to think that applied research could be possible. Such as for instance the disciplines history and Latin.