What are those who believed in the Prophet (peace and blessings be upon him) during his lifetime but did not see him called, and are they considered among the Companions?

These individuals are considered among the Tabi'un (successors), not the Sahabah (companions), because they did not accompany the Prophet, peace and blessings be upon him, nor did they see him. A Tabi'i is one who narrated from the Sahabah or lived during their time. As for a Sahabi, it is one who met the Prophet, peace and blessings be upon him, while believing in him, and died upon Islam.