For cystic acne treatments would include antibiotic creams and other topical solutions that would eliminate bacteria on the skin. Salicylic acid is another product used for cystic acne. Its helpful in killing bacteria and removing dead skin cells. In short, the treatments for cystic acne are similar to hormonal acne.
As for nodule acne, this type of skin condition cannot be treated with topical products. Usually, treatment would include oral medications such as isotretinoin (scar prevention). Other treatments would include oral antibiotics (secondary bacterial infection), adalimumab (resistance severe disease), and systemic corticosteroids (reducing inflammation).
With that being said, hormonal acne, cystic acne, and nodule acne somewhat share the same type of treatments which addresses bacteria and inflammation. Fungal acne, on the other hand, is more focused on treatments that address fungi.
If you want more clarification regarding the difference between fungal acne and other types of acne, we highly recommend you consult with a dermatologist.
It is important to know the different types of acne because this would help you identify what treatments you should be using on your skin, as advised by your doctor. Remember that fungal acne is different from other types of acne and would therefore require different types of treatments. It would also be better to have your skin checked by a dermatologist if, despite interventions, your acne problem is not resolving.