Ujjāyī vs. Free Breathing in Ashtanga Yoga (Hatha Yoga Pradipika) by Elise Espat

Q:  Is Ujjāyī the same as "free breathing with sound"?

A: No.  They are different. 

Ujjāyī is a Kumbhaka (breath retention). 

When we apply the Tristhana (asana, breathing, looking place) during our Ashtanga yoga practice, we use "free breathing with sound".  Each breath leads to the next with no retention.

So, what's the difference?  Explanation below from the Haṭha Yoga Pradīpikā (हठ योग प्रदीपिका).

Notice that one may define Kumbhaka as the retention of breath.   

 

बद्ध-पद्मासनो योगी पराणं छन्द्रेण पूरयेत |
धारयित्वा यथा-शक्ति भूयः सूर्येण रेछयेत || ७ ||
पराणं सूर्येण छाकॄष्ह्य पूरयेदुदरं शनैः |
विधिवत्कुम्भकं कॄत्वा पुनश्छन्द्रेण रेछयेत || ८ ||

baddha-padmāsano yoghī prāṇaṃ chandreṇa pūrayet |
dhārayitvā yathā-śakti bhūyaḥ sūryeṇa rechayet || 7 ||
prāṇaṃ sūryeṇa chākṝṣhya pūrayedudaraṃ śanaiḥ |
vidhivatkumbhakaṃ kṝtvā punaśchandreṇa rechayet || 8 ||

Sitting in the Padmâsana posture the Yogî should fill in the air through the left nostril (closing the right one); and, keeping it confined according to one's ability, it should be expelled slowly through the sûrya (right nostril). Then, drawing in the air through the sûrya (right nostril) slowly, the belly should be filled, and after performing Kumbhaka as before, it should be expelled slowly through the chandra (left nostril). 
-HYP chapter 2.8

Notice that Ujjāyī is one of the eight Kumbhakas.

अथ कुम्भक-भेदाः
सूर्य-भेदनमुज्जायी सीत्कारी शीतली तथा |
भस्त्रिका भरामरी मूर्छ्छा पलाविनीत्यष्ह्ट-कुम्भकाः || ४४ ||

atha kumbhaka-bhedāḥ
sūrya-bhedanamujjāyī sītkārī śītalī tathā |
bhastrikā bhrāmarī mūrchchā plāvinītyaṣhṭa-kumbhakāḥ || 44 ||

Kumbhakas are of eight kinds, viz., Sûrya Bhedan, Ujjâyî, Sîtkarî, Sîtalî, Bhastrikâ, Bhrâmarî, Mûrchhâ, and Plâvinî. 

-HYP chapter 2.44

Conclusion:
If Ujjāyī is one of the eight Kumbhakas and Kumbhakas are breath retentions, then Ujjāyī is a breath retention.  If our breathing during practice does not include breath retentions, then it cannot be called Ujjāyī.

Further, in 2.51 and 2.52 the method for Ujjāyī is described and includes the instruction to restrain the breath:

pūrvavatkumbhayetprāṇaṃ rechayediḍayā tathā |
śleṣhma-doṣha-haraṃ kaṇṭhe dehānala-vivardhanam || 52 ||

Since Ujjāyī is a Kumbhaka, it makes sense that it would include instruction for breath retention.

So, in our practice, we are only "breathing freely with sound".

 

Part 2:  A look at the Gheraṇḍa Saṃhitā (धेरंड संहिता)