Following are the synonyms of disease:

Shloka- Ashtang Hridaya Ni 1/1

Rog
Disease is also called Roga since it gives Ruja (pain).

Papma
It is born from 'pap' (sinful acts).

Jvara
It is by nature tormentive.

Vyadhi
Since it brings about different kinds of abnormalities which cause Dukha (distress).

Dukha
When inflicted with a disease one experiences Dukha (unhappiness).

Amaya
Since one of its causes is Ama (undigested improperly processed metabolites).

Yakshma
Since many a times it manifests itself as a group of symptoms (syndrome).

Atanka
Since when inflected with a disease life becomes miserable .

Gada
Since it ma be produced by multiple causes at the same time.

Abadha
It produces constant discomfort to our body, mind or sense organs.

Classification

Samanyaj
The disease caused due to vitiation or disequilibrium of any one, two or three Doshas refers to samanyaj vyadhi.

Example: Anemia that can be caused due to the vitiation of either of Vata, Pitta or Kapha Dosha or all of them.

Nanatmaj
The disease caused due to vitiation or disequilibrium of one particular Dosha.

Example: Grudhrasi(sciatica), Kamala(jaundice), Medorog(obesity) due to vitiation of Vata, Pitta, Kapha Doshas respectively.

Sadhya and asadhya

Shloka - charak su 10/9

It refers to curable diseases and Asadhya means incurable.

Sadhya is divided into following two categories:

Sukhasadhya
Easily curable (Within A Short Span Of Time)

Kruchchhasadhya
Difficult to treat

Asadhya is divided into following two categories:

Yapya
Where in treatments or remedies applied afford relief to the patient but within a short span relapse again. So also the patient is relieved when he is on medication but if the medication is stopped the disease relapses.

Pratyakheya
Irremediable i.e. remedies applied in no way give relief to the patient.

Agantuj
External factor causes a disease.

Example: poison, accidents, heat stroke etc.

Nijroga
Disequilibrium or disharmony of the Doshas are responsible for the disease.

Manas (psychiatric disease)
Disequilibrium of the Rajas & Tamas Guna influence Mana (mind) and inflict disease.