There is no short answer for this question. Although I can say qPCR and RT-qPCR are basically the same and both are used for realtime detection of amplification. RT-PCR and PCR are different methods for end-point detection of RNA and DNA amplification, respectively.
Conventional PCR gives qualitative end point results for DNA amplification.
Reverse Transcriptase (RT)-PCR: gives information of mRNA, which is reverse transcribed to cDNA and then amplified.
qPCR (Real-Time PCR) and RT-qPCR , has become increasingly important in clinical diagnostics and research laboratories due to its capacity for generating quantitative results. Here, the fluorescence signal increases proportionally to the amount of replicated DNA and hence the DNA is quantified in “real time”.
DNA replicates and stores genetic information. It is a blueprint for all genetic information contained within an organism. So PCR /qPCR has application for getting information of DNA e.g. mutation analysis.
Messenger RNA (mRNA) copies the portions of genetic code by a process called as transcription, and transports these copies to ribosomes, which are the cellular factories that facilitate the production of proteins from this code. Hence, for knowing any details on mRNA which is later converted to proteins RT-PCR / qRT-PCR is performed.
Some applications are mentioned in following articles: