There are several diseases that are related to Feline Asthma. Lungworms, heartworms, upper & lower respiratory infections, lung cancer and cardiomyopathy can all mimic asthma symptoms and therefore should be ruled out. Please note that these diseases, particularly heartworm, react favorably to steroid treatment, so you cannot assume that it is in fact asthma simply from a favorable reaction to treatment. 

Lungworms
Lungworms are parasitic nematodes that require an intermediate host for infection to cats. The route of infection for lungworms is oral. Lungworms can be ruled out by a fecal test.

Heartworms
Heartworms are parasitic nematodes that require an intermediate host for infection to catsThe route of infection for heartworms is through the skin; they are transmitted to cats by mosquitoes that carry the larvae. Heartworm does cause coughing in some cats. Heartworms are difficult to diagnose. There are two kinds of tests for feline heartworms: antigen and antibody. The antibody test only indicates exposure not infection with worms, which can lead to false positives. The antigen test looks for a specific hormone that the worms release and so it is evidence of a current infection. However, because most cats have a very low worm load, and presumably low circulating antigen levels, the odds of a false negative are good. Cardiac ultrasound is additional diagnostic tool that can also assess the current health of the heart as well as provide an idea about worm load.

Because of a lack of substantial symptoms associated with heartworm disease in cats and the high risk involved in treatment, most often it is recommended that the cat begin heartworm prevention (Heartgard/ivermectin) to prevent the current worms from reproducing while waiting for them to complete their lifespan which is about two years. The death of the worms may be uneventful so that the body absorbs their remains or may cause a cardiovascular obstruction that could be fatal.

Heartgard (active ingredient ivermectin) works to kill the larvae that circulate in the blood vessels before developing into the adult heartworm. Ivermectin has no effect on adult heartworms. Ivermectin toxicity in cats is only a concern at much higher doses than Heartgard provides, is more common when it is injected subcutaneously, and such toxicity is unrelated to current infection with heartworms.

Lung Cancer - from Merck
The respiratory system can be a host to many different types of tumors and cancers.

Cardiomyopathy

Prolonged coughing can sometimes lead to heart trouble by enlarging and thickening the heart. This is not true cardiomyopathy but may show as slightly enlarged heart on ultrasound.

True cardiomyopathy will present with the heart as an abnormal shape and fluid may be detected in or around the lungs. If a large amount of fluid is present around the lungs, it may be necessary to remove it and take more radiographs because the presence of this fluid interferes with evaluation of the heart. Ultrasound and electrocardiogram (EKG) are common tests for cardiomypopathy.