بسم الله الرحمن الرحيم
The science of Ḥadīth: is a study of the rules and principles which seek to explain the condition of the sanad (chain of narration) and the matn (text) of aḥādīth (narrations), and to verify its authenticity as to whether it is maqbūl (accepted) or mardūd (rejected).
Ḥadīth (pl. aḥādīth) - الحديث: linguistically means ‘new’ or ‘speech’. From a technical discussion under the topic of hadīth sciences; it means a narration attributed to the Prophet ﷺ, either about what:
1. he said, or
2. he did, or
3. he tacitly approved.
Other words such as khabar (الخبر) and athar (الأثر) can sometimes be used interchangeably with hadith, but different muḥadithīn (hadīth scholars) have different definitions. The word khabr (pl. akhbār) linguistically means news, and technically some have said it is a synonym of hadith, whilst others have maintained that a hadith is what is attributed to the Prophet ﷺ whilst a khabar is a narration attributed to other than him, such as his Companions. Yet others have said that a khabar can be attributed either to the Prophet ﷺ or to those other than him, such as his companions.
Athar (pl. āthār) linguistically means remnant or residue. Technically, some have said that it is synonymous to hadith, whilst others have maintained that it is a narration attributed either to the Companions of the Prophet ﷺ or their tābi’īn (the following generation after the Companions).
Sanad - السند: linguistically means support or pillar, and it is termed as such because the hadith is dependent on it and is supported by it. Technically it refers to a chain of individual narrators which attribute the matan of the hadith to the Prophet ﷺ. Isnād (الإسناد) on the other hand is the verbal noun from the same root as sanad; some have said that it refers to the actual chain of narrators and thus is synonymous to sanad, whilst others have said that isnād refers to attributing the hadith to its narrator by mentioning the chain of narration.
Matan (pl. mutūn) المتن: linguistically means what is strengthened and surfaced from the earth. Technically it refers to the text of a hadith distinguished by the sanad.
Musnid (with a kasrah on the nūn) - المسنِد: This is the active participle (اسم فاعل) from the same root as sanad, and it refers to the individual who narrates the narration with a sanad, such as Imām Bukhāri. Musnid is also synonymous with the term rāwi (narrator).
Musnad (with a fatḥah on the nūn) - المسنَد: this is the passive participle (اسم مفعول) from the same root as sanad, and it refers to a hadith that is supported by a sanad which is connected from the beginning and end, and is muttaṣil (connected without any gaps in between) and marfū (elevated to the Prophet ﷺ). Musnad can also refer to book which is a compilation of narrations from each narrator separately. Others have said that it is synonymous to sanad and thus is a maṣdar mīmī (a verbal noun that begins with a mīm).
Muḥaddith – المحدّث: refers to an expert of hadith sciences who has a deep knowledge of narrators and narrations.
Ḥāfiẓ (pl. Huffāẓ) الحافظ: According to majority of the muḥadithīn, it is synonymous to the muḥaddith. Some have said that it refers to one who is more knowledgeable than the muḥaddith.
Ḥākim - الحاكم: refers to the one who has encompassed all aspects of hadith sciences. Such as al-Ḥākim Abu ‘Abdillah an-Naysābūrī.
Hope that was beneficial.
May Allah the Exalted reward you and I both.