The Sanskrit word Siddha refers to a practitioner who has advanced far enough to have attained certain spiritual powers known as siddhis.
The word Siddha further refers to the broader tradition of attained Adepts which was the historical forerunner of the Nath Sampradaya.
Within the International Nath Order, Siddha names the person and the older stream, not the power and not membership in the Order. Shri Gurudev Mahendranath placed the Naths as a development of that Siddha–Avadhut line, after Siddhas and Tantrics had already been drawn into one order. A Nath or Devi is one who has received INO initiation. That transmission starts the work. It does not, by itself, make the initiate a Siddha. In INO usage an Adept is one who has attained to the sphere of Siddhi. Mahasiddha is a rarer title still. Do not read Siddha as another word for Siddhi.