Mukti does not necessarily always mean Moksha. it depends on how the word is used in the sentence.
For example in the words like Rogamukti (freedom from disease), Rinamukti (freedom from debt) etc it does not mean Moksha at all but simply freedom or to get rid off.
But when used in that context then Mukti means Moksha. Then those are just two different words which are used to refer to the same thing.
For example, we have the following verse from Devi Mahatyam:
सर्वभूता यदा देवी भुक्तिमुक्तिप्रदायिनी ।
त्वं स्तुता स्तुतये का वा भवन्तु परमोक्तयः ॥
sarvabhūtā yadā devī bhukti-mukti-pradāyinī ।
tvaṃ stutā stutaye kā vā bhavantu paramoktayaḥ ॥
When you [who are] Devi, are all of manifestation, are a giver of nourishment [in this world and] liberation [from this world], are the praised one, [then] for [your] praising, whatever can be great utterances.
That is, Devi, you are beyond my ability to find words to praise you. greatest of the great words fall short of praising you. [but even then let me try].
The word by word meaning is as follows:
sarvabhūtā = all (sarva) manifestation, people, world ( bhūta) yadā = when devī = goddess bhukti = consumption (food, needs etc.) mukti = liberation (of soul from bondage) pradāyinī = giver (fem.)
tvaṃ = you [are] stutā = [THE] praised one stutaye = for praising [you] kā = what vā = or, ever, (to indicate what ever could be ..) bhavantu = can be paramoktayaḥ = greatest (parama) utterances (uktayaḥ)
So, here Mukti is used to mean Moksha.
Further, we have from the starting verses of the Phalasruti of the Durga Satanama Stotram, found in the Viswasara Tantram:
- Ya idam prapathen nityam durganamasatashtakam |
- Na sadhyam vidhyate devi trishu lokeshu parvati ||
- Dhanam dhanyam sutam jayam hayam hastinameva cha |
- Chaturvargam tatha chante labhen muktincha shwashatim ||
The meaning of these verses is "One who daily recites this Stotra comprised of hundred names of Goddess Durga there is nothing in the three worlds that he can not achieve. Also, he gets worldly pleasures like wealth, crops/food, wife, son etc. He obtains the Chaturvarga (i.e Artha, Kama, Dharma etc) and at the end obtains eternal Mukti."
Here again, Mukti means Moksha.
Yet another verse from Kularnava Tantram's third chapter:
- Salokyapramukham devi labhenmuktim chaturvidham |
- Satyametanna sandehah sadhaka kulanayike ||
This verse is describing the result that one obtains by chanting a particular Mantra for four hundred times. It says that such an aspirant gets four kinds of Muktis or Moksha.
So, here too Mukti means Moksha.
(Four kinds of Muktis are Salokya, Sarupya, Sarshti, and Sayujya )
There can be plenty of such references. Here are a few more from the Yogic text called Hatha Yoga Pradipika.
- Sarveshāmeva bandhānām uttamo hyuddīyānakah
- Uddiyāne drdhe bandhe muktih svābhāvikī bhavet||
Of all the Bandhas, Uddiyâna is the best; for by binding it firmly liberation comes spontaneously.
- Sahajoliriyam proktā śraddheyā yoghibhih sadā
- Ayam śubhakaro yogho bhoghayuktoapi muktidah||
This is called Sahajolî and should be relied on by Yogîs. It does good and gives moksa.
So, in such contexts, Mukti, Moksha, Kaivalya etc are all synonyms.