Any rRNA analysis would be sufficient. In a scenario where immediate instrumentation in not available a gram stain would separate the gram positive Actinobacteria from the gram insensitive mycelial fungi except in cases of yeasts. Visually actinobacterial mycelia lack the highly specialized radial growth observed in fungi in the form of aerial and substrate mycelial expansions. Although differentiated structures such as spores, spore chambers etc can be observed in actinobacterial mycelial growth. Under a microscope the endospore forming actinomyces or actinobacteria will not possess any pseudoseptation that fungal hyphae do. The bacteria is prokaryotic while the fungi are eukaryotes. Most importantly you can inhibit the growth of either of them using antibiotic or antifungal compounds. Whichever is not arrested is the other than what the antibiotic was applied for.

Regards,

Dr. Abhishek Mukherjee

If you can, have a look at cellular diameter. Actinomycetes are miniature diameter compared to fungi, even if they branch.