The difference in the process of creation is due to Kalpa-Bheda.
According to Shiva Maha Purana, (Chapter 13, Vayavivasamhita, Shiva Purana).:
Vayu said, I shall narrate how Rudra was born and how Brahma and Vishnu were born from each other. The three are Atmans as causes of born of Mahesvara; they are cause of creation, sustenance and annihilation of the Universe consisting of mobile and immobile beings. Endowed with great qualities they are sanctified by great Lord. Presided over by his Shakti, they can perform their activities. Brahma can create, Vishnu can protect and Rudra can annihilate. But they rivaled with one other. Desirous of excelling one other they propitiated their father the Supreme Lord by means of penance. Attaining all around favor of Lord at outset in Previous Kalpa, Rudra created Brahma and Vishnu. In another Kalpa, Brahma created Vishnu and Rudra. In another Kalpa, Vishnu created Brahma and Rudra. Thus in different Kalpas, Brahma, Vishnu and Rudra desiring mutual benefit are born of one another. Based on the events in their respective Kalpas, their process in being the cause of origin of one other is extolled by Sages.
So, in different different Kalpas, Lord Brahma, Lord Vishnu snd Lord Rudra Creates, Preserve and Destroy the Universe.
As for Purusha Shuktam, this Supreme Purusha (Cosmic Being according to your question) is a Part of Parambrahma. But different sects identify him differently as per as their beliefs. Its same as the following rig-vedic verse.:
एकं सद विप्रा बहुधा वदन्त्यग्निं यमं मातरिश्वानमाहुः || (Rig-Veda 1:164:46)
ekaṃ sad viprā bahudhā vadantyaghniṃ yamaṃ mātariśvānamāhuḥ ||
God (Truth) is only One, but wise and saints call him by many different names.