I would like to know how many types of mukti are there. Also, is mukti the same thing as moksha? If not, what is the difference between those two?
If there are different types of mukti, is any type considered superior over the other?
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Mukti and Moksa mean the same. The meaning is to cast off, abandon, release. It is the process of releasing the soul from the material bondage and hence the common word in english is liberation.
Different kinds of liberation are discussed in Srimad Bhagavatam Canto 3, chapter 29, verse 13
A pure devotee does not accept any kind of liberation — salokya, sarsti, samipya, sarupya or ekatva — even though they are offered by the Supreme Personality of Godhead.
In regards to if one is considered to be higher than the others it depends on who you ask. A personalist(Vaishnava) doesn't desire ekatva, merging into the existence of the Supreme Lord or impersonal Brahman. From a Gaudiya Vaishnava perspective there are different mellows, rasas, a devotee exchanges with Lord. The mellow of servitude, friendship, parental and conjugal. It is said that the mellow of conjugal relationship like in the case of Radha and Krishna constitutes the highest and most intimate relationship with the Supreme Lord. Of course the nature of any relationship with the Lord is full of ecstasy and each devotee thinks himself to be an insignificant servant of the Lord and His servants, so a devotee doesn't think he is superior to others.