What is the main difference between Avadhuta and Jivanmukta?
Literally the word Avadhuta means "one who has shaken off" the worldly existence. So, it denotes a free, liberated being. And, Jivanmukta means the same too viz: "one who has attained liberation while still living".
Various kinds of liberation are mentioned like Jivanmukti (which is achieved while living), Videhamukti (which is achieved not while living but after death) and Kramamukti (which will happen for sure sometime in the future but not certain exactly when).
Therefore, there is basically no difference between an Avadhuta and a Jivanmukta. Both has achieved the knowledge that liberates and they have done so while still living.
Lord Shiva gives the following definition of an Avadhuta which further proves my point:
tattvamasya-artha-siddhatvAt avadutohabhidhiyate ||
Since he is immutable/imperishable (akshara), best among/most excellent (varenya), since for him the worldly bondage are all removed (dhuta-samsAra-vandanat) and since he has realized the meaning of "Tvat Tavam asi" (you are that) -- he is called Avadhuta.
KulArnava Tantram 17.24
Now, Avadhuta is also the name of a class of Sanyasis (ascetic) as mentioned in some minor Upanishads:
 "There are six types of renunciation: Kuticaka, Bahudaka, Hamsa, Paramahamsa, Turiyatita, and Avadhuta.55 A Kutlcaka has a topknot and a sacrificial string, carries a staff and a water pot, and wears a loincloth and a patched garment. He is devoted to honoring his father, mother, and teacher, to the use of articles56 such as a pot, a spade, and a sling [LSU 21, n. 27], and to the practice of eating food obtained from one place. He wears a white vertical mark on his forehead and carries a triple staff.
From the Narada Parivrajaka Upanishad
Among these types, the Avadhuta and Turiyatita are considered as the highest kind and they are considered as free while living or in other words as Jivanmuktas.
"To those who renounce at a time of mortal danger and to Kuticakas belong the earthly world and the atmospheric world, respectively.
To Bahudakas belongs the heavenly world, to Hamsas the Penance-world, and to Paramahamsas the Truthworld [ArU 4, n. 3].  To Tunyatitas and to Avadhutas belongs the attainment of liberation in their very selves through the deep meditation on their own true nature in the manner of the wasp and the worm
We also have the Avadhuta Gita where the Avadhuta refers to Lord Dattatreya who is the best example of a Jivanmukta.
So, although two different words, both refer to a "liberated while living being".
The word 'Avadhuta' has different meanings.
- It is the word used for the ones who have taken sannyasa in the Tantric way:
AvadhutAshramo devi kalau sannyasa uchchyate:O Devi! In the age of Kali, sannyasa-ashrama is called Avadhuta (Mahanirvan-Tantra,8/221).
- One meaning of Avadhuta is
yo vilanghya AshramAn dharmAn Atmanyeva stitah puman/ ativarnashrami yogi avadhuta sa uchchyate : Meaning : He who have renounced all Ashrama-dharmas and stays immersed in the Self is called Ativarnashrami or Avadhuta.
- Avadutas are four types of aspirants:
Saiva-Avadhuta, Brahma-Avadhuta, Hansa-Avadhuta (also Paramahansa-Avadhuta) and ParivrAt (Apurna-Bhakta-Avadhuta).They use five titles: Vana, Aranya, Bharati, Giri and Puri.
- Avadhuta also means householder monks (grihasta-Avadhuta) .
(Reference: Bangiya Shabdakosha, Haricharan Bandyopadhtay, Vol. 1).
Avadhuta refers to Sadashiva too as per the Mundamala-Tantra.
According to Sridhara Swami, Avadhuta means the one whom people have ignored and rejected.
The Nirvana-Tantra clarifies the features of an Avadhuta as
learned in different scriptures, efficient in different (Tantric) worships, always sseing all women as the Ishta-Devi, the most wise, controller of all senses, equal to all and everything, hands raised upwards, hair unbound and body fully naked, always roaming at different places, worshipping with great devotion regularly, worshipping Guru and Ishta and always doing yoga internally.(parva 14).
'Jivanmukta' is the word for someone who has been liberated while living.The Sarva-Darsana-Sangraha (9/2) defines Jivanmukta as
Who has realised the Tattva of the Self, and has been freed from the delusion of Maya and have been consumed the 'praravdha karma'-s, is liberated while being alive.Then He is called Jivanmukta.
So Jivanmukti is the Supreme state of realisation or illumination and is not necessarily related to Tantra.
The 'Jivanmukti-Gita' defines Jivanmukta as
The mind of a person Who always meditates on the Supreme Self as the sky all around is called Vijnana. The one whose mind dissolves after being in the vijnana state is a Jivanmukta.
He Who knows that The Supreme Consciousness resides in every thing and every being is a Jivanmukta.
The Shiva-Samhita says
He Who always sees The One in every being and everything and is beyond bondage or liberation is a Jivanmukta (5/173).
According to the Yoga-Vasistha also, a Jivanmukta is the knower of the Supreme Self.
So 'Avadhuta' has different meanings from a person rejected by all to a Realised Soul and even Shiva.Some Avadhutas are mentioned as worshipping regularly as seen in the Tantra.So Avadhuta xan be God, can be Jivanmukta or a Tantric monk or householder.
A Jivanmukta needs no further spiritual activity. He has already reached the goal and enjoying the fruits of all His penance and good deeds.
Reference : Sastramulak Bharatiya Shaktisadhana, Upendrakumar Das, RMIC, Vol.1, Mukti o tahar Sadhan, Vipin Bihari Ghoshal (1881).