Mantras are of 3 basic types viz-masculine,feminine and neutral.Those ending with Hum or Phat are masculine,those ending with Swaha are feminine in nature and those ending with Namaha are neutral mantras.
From Narada Purana:
The basic forms of Mantras are of ‘Stree’ (Feminine), Purusha
(Masculine) and Napumsak (Neuter). The Stree Mantras end up with
‘tha’or ‘swaha’; Purusha Mantras end up with ‘Hum’ and ‘Phut’; those
Mantras end up with ‘Namah’ are used in Napumsak Mantras. The various
Mantras are utilised in the context of six ‘Karmas’ deeds) viz.
‘Shanti’ (Peaceful purposes), ‘Vashya’ (subjugation), ‘Stambhana’
(paralizing), ‘Dwesha’ (creating hatred), ‘Ucchhanana (uprooting) and
While doing PitruYajnas(sacrifices to Manes or Pitrus) the mantras have Swadha at the end.
While doing DevaYajnas(oblations to Devas or Gods) the mantras have Namaha,Swaha or Vashat at their end.
And,while doing Manushya Yajna(oblations to mankind) Hanta is used similarly.
"Swaha," " Vashat" and "Namah," [these three] are for the Celestials ;
" Swadha " is for the departed Manes ; and " Hanta" is for mankind.
(12) Therefore one should daily make offerings to the Pitris by
reciting " Swadha" Some say the word " Namah " may be added to it. But
Goutama [says], "not so." (13)
Katyana Smriti,Chapter 13,Verse 13.
The verse "Om Jayanti Mangala kali Bhadrakali Kapalini Durga Kshama Shiva dhatri swaha swadha namostute" appears in the Argala Stotram which is to be recited before reciting the Devi Mahatyam(present in the Markandeya Purana).
जयन्ती मङ्गला काली भद्रकाली कपालिनी । दुर्गा शिवा क्षमा धात्री स्वाहा
स्वधा नमोऽस्तु ते ॥२॥
Jayantii Manggalaa Kaalii Bhadrakaalii Kapaalinii | Durgaa Shivaa
Kssamaa Dhaatrii Svaahaa Svadhaa Namostu Te ||2||
2.1: Salutations to Jayanti (Who is Ever-Victorious), Mangala (Who is the bestower of Auspiciousness), Kali (Who is beyond Kala or Time),
Bhadrakali (Who is the controller of Life and Death, being beyond Kala
or Time), Kapalini (Who wear a Garland of Skulls),
2.2: Salutations to Durga (Who is Durgati-Nashini), Shiva (Who is Ever-Auspicious and One with Shiva as His Consort), Kshama (Who is an
embodiment of Forbearance), Dhatri (Who is the Supporter of all
Beings), Swaha (Who is the final receiver of the Sacrificial
Oblations to Gods) and Swadha (Who is the final receiver of the
Sacrificial Oblations to Manes); Salutations to You.
The implication is whether one is doing a Pitru Yajna (with Swadha) or a Deva Yajna(with Swaha) the oblations are eventually reaching the Divine Mother Devi Durga only.