The terminology used differs by region.
The majority of scholars use the term hadith to describe any such narration that either quotes a speech, describes an action, or documents an approval by either the Prophet ﷺ or any of his companions. When it is a hadith attributed to the Prophet ﷺ, it is called marfū' (Arabic: مرفوع). When it is a hadith attributed to a companion, it is called mawqūf (Arabic: موقوف). Either type can be graded in terms of its authenticity as sahih, hassan, da'īf, mawdū', etc. This is based on the definitions provided by An-Nawawi in his book At-Taqrīb wa at-Taysīr, pp. 32 and pp. 33 (Arabic only).
As for the terms used by other scholars, mainly from Khorasan, they use khabar to mean hadith marfū' and athar to mean hadith mawqūf (note that khabar is more general than just hadith marfū'). This is documented by
in his book Tadrīb ar-Rāwi, Vol. 1, pp. 29 (Arabic only), where he also confirmed the definitions used by the majority of the scholars as defined by An-Nawawi.
It is worth noting that the above definitions are the same ones used by Ibn Taymiyyah, Ibn Hajar al-'Asqalani, and most other muhaddithīn (scholars of hadith). One of the best books that define hadith terminology is Fat'h al-Mughīth by Al-Sakhawi. In it, he defined the terms marfū' and mawqūf (Arabic only) to the same effect as above.
The books are the same books of hadith commonly used, including but not limited to the six major books.