The Padma Vyuha is often confused with the Chakravyuha, as many writers use these terms interchangeably. It is told in Mahabharata that Chakravyuha was used in the 13-th day and padma-Vyuha on 15-th day. Are they the same?
Both battle formations appear to be different. The Critical Edition of the Mahābhārata uses "Cakravyūha" (wheel formation) to describe the formation Droṇa constructed on the 13th day of the war in which Abhimanyu was killed.
07,033.012 saṃjaya uvāca
07,033.012a cakravyūho mahārāja ācāryeṇābhikalpitaḥ
07,033.012c tatra śakropamāḥ sarve rājāno viniveśitāḥ
Sanjaya replied, “O great king! The preceptor created the chakra vyuha. All the kings, who were Shakra’s equal, were assembled in it....
(English translation from The Mahabharata: Volume 6 by Bibek Debroy)
The Southern Recension of the Mahābhārata however calls the same, Padmavyūha (lotus formation). And this is probably why the terms are often used interchangeably.
7.34. adhyAyaH 034
Mahabharata - Drona Parva - Chapter Topics
droNena padmavyUharachanA.. 1 ..
sa~njaya uvAcha. 7-34-0x
sthiro bhava mahArAja shokaM dhAraya durdharam.
mahAntaM bandhunAshaM te kathayiShyAmi tachChR^ishu.. 7-34-1
padmavyUho mahArAja AchAryeNAbhikalpitaH.
tatra padmopamAH sarve rAjAno viniveshitAH.. 7-34-2
On the 14th day, to protect Jayadratha, Droṇa constructs an even more intricate formation, part padma (lotus) and part śakaṭa (cart) but makes no reference to the Cakravyūha he constructed the previous day so it's possible this is an entirely different formation.
Chapter 1030 (53)
07,053.027a śakaṭaḥ padmapaś cārdho vyūho droṇena kalpitaḥ
07,053.027c padmakarṇikamadhyasthaḥ sūcīpāśe jayadrathaḥ
07,053.027e sthāsyate rakṣito vīraiḥ sindhurāḍ yuddhadurmadaiḥ
Drona will construct a vyuha at the rear. Half of this will be in the form of a cart and half in the form of a lotus. There will be an array in the form of a needle in the midst of the pericarp of the lotus. Jayadratha, the king of Sindhu who is unassailable in battle, will be stationed there, protected by brave ones.
Debroy, Bibek. The Mahabharata: Volume 6 (pp. 61-62)