Have come across the phrase Dhyana Mantra several times in context of Durga puja, Kali puja. But what is the difference between a Mantra and a Dhyana Mantra? Can it be different for the same deity? What is the concept behind Dhyana Mantra?
This is a good question.
The word 'Mantra' has many connotations. I am providing a few from sanskritdictionary.com:
mantraḥ मन्त्रः [मन्त्र्-अच्] 1 A Vedic hymn or sacred prayer (addressed to any deity), a sacred text; (it is of three kinds:-it is called ऋच् if metrical and intended to be loudly recited; यजुस् if in prose and muttered in a low tone; and सामन् if, being metrical, it is intended for chanting). -2 The portion of the Veda including the Samhitā and distinguished from the Brāhmaṇa; q. v. -3 A charm, spell, an incantation; सो$हमस्मि मन्त्र- सिद्धः Dk.54; न हि जीवन्ति जना मनागमन्त्राः Bv.1.111; अचिन्त्यो हि मणिमन्त्रौषधीनां प्रभावः Ratn.2; R.2;32;5.57. -4 A formula (of prayer) sacred to any deity, as ओं नमः शवाय &c. -5 Consultation, deliberation, counsel, advice, resolution, plan; तस्य संवृतमन्त्रस्य R.1.2; मन्त्रः प्रतिदिनं तस्य बभूव सह मन्त्रिभिः 17.5; Pt.2.182; Ms.7.58; मन्त्रपूर्वाः सर्वारम्भाः Kau. A.1.15; (Reference: https://www.sanskritdictionary.com/?iencoding=iast&q=मन्त्र&lang=sans&action=Search)
So Mantra can be Vedic, like the Rig-Mantras, the Gayatri (Savitri) Mantra etc,or it could be a Tantric/Pauranic Mantra.
Normally by 'Mantra' we mean the 'Bija-Mantra.Any 'Bija-Mantra' must have four aspects : Rishi (The Seer Who first saw the Mantra), Chhanda (Metre), DevatA (the Deity of the Mantra) and Samprayoga (the application/results of the japa of the Mantra). The Gautamiya-Tantra says:
rishis_chhando_aparijnAnAn_na mantraha falabhak bhavet/daurvalyam yati mantraNAm viniyoga-ajAnatAm// meaning : Without knowledge of the rishi, chhanda and viniyoga, the Mantra becomes weak and it does not bear any fruit.
For example, in the Mantra of DakshinA KAli, the Rishi is Bhairava, the Chhanda is Ushnik, DevatA is DakshinA KAli. The Viniyoga can be 'Chaturvarga-fala-lAbha ie obtaining dharma, artha,kAma and moksha.It could be fulfilling any spefic desire or getting Moksha alone also.
So it must first be made clear that mantra can jot be constructed. It appears to the Rishis.We will go to the topic in some detail a bit later.
Alternatively, we also get to know about six bodies of the mantra: Rishi, Chhanda, DevatA, Bija,Sakti and Kilaka. For example, again for the DakshinA KAli Mantra
Rishi is Bhairava, Chhanda is Ushnik, DevatA is DakshinA KAli, Vija is Hrim, Shakti is Hum and Kilaka(also known as adya-bija is krim. (KAli-tantra,1/8-9)
According to TripurA-siddhAnta
a mantra has seven bodies: rishi, chhanda, Bija, kilaka,Shakti, Agna-nyAsa, and DhyAna (DipikA of SrividyA-ratnasutram,1)
The above mentions the DhAna-Mantra.
According to the Gayatri-Tantra (Brahmana patala 2), a mantra has five bodies
AvAhan (welcoming), DhyAna,smarana(meditating), samarpana(offering) and visarjana(biding farewell).
Now let us see the definition of Mantra from the scriptures.
The first definition is from YAska.According to Him,
mantrA_mananAt (nirukta 7/12) meaning that by which one can contemplate (manana) is called mantra.
According to SrividyA-ratnasukta, 'Man' signifies 'Manana' and 'Tra' signifies trAna (relief/ removal of bondage). According to the PingalA-mata-Tantra, from which one can contemplate on the real knowledge about the world and get his wordly bondages removed is mantra.Gayatritantra defines mantra as that which washes off all sins and yields bliss and liberation is mantra.
Now the details about the Rishi. This is important because in these days we see many constructed mantras being given and chanted. Our scriptures do not allow this at all. It is clearly mentioned that
yena yat rishinA drishtam siddhih prAptA cha yena vai/mantrena tasya tat proktam rishe bhAbas tadArshakam// (tika to 1), meaning that to whom the mantra appears is rishi.He also becomes siddha in that mantra. The source of mantra must be divine, that is it is not man-made.
So Mantra is actually a verbal form of the Deity, Who appears in front of the seer.
The DhyAna-mantra gives detailed dsecription of the form of the deity including sex, complexion, nature, number of arms, posture, weapons and mudras etc.
Yes, dhyAna-mantra can be different for tge same deity. For example, Kali has eight to twelve or even more forms.DakshinA-KAli has two dhyAna-mantras.Everything is there mentioned clearly in the scriptures.
Some Mantras are called Purusha-Mantras (where the deity is Male) and Stri-Mantra(where the deity is female). All other mantras are napumsaka(of neuter gender).
There are many other classifications of mantra like siddha,sAddhya,susiddha and Ari,Dhani and Rini, pinda,kartari,bijaka etc etc.
Hope this answers your question.The best reference is the 10th chapter of Sastramulak Bharatiya Shaktisadhana by Upendrakumar Das, RMIC, vol.1. Unfortunately the book has not yet been translated to English so far as my limited knowledge goes.