Atma also pronounced atman is the Prana, spirit manifesting human form. Before manifesting any form an Atma was attributeless, remained inert as it is. The moment it manifests a form it is called Jeevatma. The Atma within a Jiva (living being) is of the same essence as in human beings.
Primarily it is our Atma that is the master and controller of human life. As no Atma can purify itself of its own, it needs a medium a body to cleanse itself of dross impurities within. When life supporting planets like mother earth evolved all Atma immediately started manifesting body on mother earth. Body after body, manifestation after manifestation this cosmic journey of life for an Atma continues unabated.
Jiva also pronounced Jeeva is a term used for a living being whether human or lower form of life.
Paramatma is the term used for God, Brahman the one and only creator of entire cosmos. We call God Almighty Paramatma because it is the collective power of all Atma in their pure form in entire cosmos. If an individual grain of sand is an independent Atma, the whole mound Paramatma. If an individual piece of puzzle is an independent Atma, the completed puzzle Paramatma.
Parmatma or Parmatman is that entity as per Bhagavad Gita explosion of which resulted in creation of present cosmos. It is an absolute fact of life on mother earth and a spiritual truth that it is God Almighty, Brahman Parmatma that exploded self with a big bang to form present cosmos.