Different things. Some people experience asthma as breathlessness or feeling starved for air, others chest tightness or chest pain, and still others hear or feel the wheezing in their chest. A few people only have cough, although they are the minority. When severe, there is usually little doubt about the diagnosis, but milder forms can sometimes be difficult to sort out.
Terrible.... People describe the sensation as "breathing through a straw." it feels like there is not enough air in the room. It is a very scary sensation.
Terrible.. Asthma attacks are usually fairly quick in onset, though if you're asthma is not well-related it may be hard to tell what's an attack and what is just uncontrolled asthma. Symptoms are usually shortness of breath, coughing, chest tightness, feeling like it's hard to get air out of your chest, and you may hear wheezing. If these start abruptly, you may need prompt medical attention.