A tābiʿī (تابعی), Successor, is a Muslim who is not himself a Companion but met a Companion while a believer.1
Example: Ḥasan al-Baṣrī, may Allah have mercy on him, is a Successor. He was not a Companion himself; he met Companions.
Difference: A Companion's definition concerns meeting the Prophet ﷺ. A Successor's definition concerns meeting a Companion.
1. Plural form: Tābiʿīn (تابعین) is also used for several Successors.