Amnaya is another word used for Tantra. It means sacred tradition handed won by tradition. Amanya is usually applied to Vedas. Tantra, in ancient times, was regarded as the fifth Veda, which is said to be more important in the Kali Yuga that the other four Vedas. Hence the word amanya is applied to Tantra.
Tantra is also called agama and nigama. As explained in Agamarahasya (I.43), agama is that which come out from the mouth of Shiva and goes to the ears of Goddess Girija (Goddess Parvati), which it is witnessed or approved by Vasudeva. The meaning of the word nigama is not mentioned in this text. But traditionally, the word nigama is applied to those texts in which Goddess Parvati explains the Shastras to Shiva. But at many places the word agama is just used as a synonym for nigama.