Thank you for the context.The two words mean different things, just as their dictionary definitions suggest:
1. “Fig. 4A shows a presumptive species identification of 42 Aspergillus samples in three major groups.” presumptive: of the nature of a presumption – presumed in the absence of further information.
Here, the species identification has been tentatively, temporarily, made based on available information at the time. This could change with more information.
2. “Another controversial aspect of the DNA barcoding initiative relates to the number of individuals of each putative species to include in the analysis.” putative: generally considered or reputed to be.
Here, I believe that each species is generally considered to be a separate species – in other words, we’re not arguing about the classification of species here; we’re focusing on something else, i.e. the number of individuals to include in the analysis.