As stated above, breathing is the biological process of inhaling and exhaling of the gases between the cells and the environment. The mechanism of breathing involves various respiratory structures such as the windpipe, lungs and nose. Respiration, on the other hand, is a chemical process that takes place in the cell.
That would be ascomycota or sac fungi. Sac fungi are characteristically known for producing ascus. This is a sac-like structure that contains haploid spores called ascospores. Some examples of sac fungi are yeast, truffles, morels and dead man's fingers.