Though in the present Hinduism a tradition is to think Rudra and Shiva as one and the same Gods, the fact is otherwise. From religious history of Hinduism, we can easily note that both the Gods are different and each representing the opposite religious traditions...i.e. Vedic and Non-Vedic.
Shiva is the highly worshiped deity in India, having its sacred temples in millions spread across the country. Not a single town or village will be found where Shiva shrine is absent. Shiva is worshiped in the temples or in open in his Lingam (Phallic) form. His consort Shakti (synonyms Parvati, Jagdamba, Amba etc.) too is worshiped in unified form with Shiva and also independently in her abundant temples across the country. Shiva-Shakti worship can be traced back to the Indus civilization where abundant proofs of Shiva worship have been found.
Most importantly the Shiva is a non-Vedic God, having no space in Vedic religion. Rather He is ridiculed as “Phallus God” (Shisnadeva) in Rig Veda. All non-Vedic elements can be seen in Shiva images such as serpent in the neck, wearing tiger skin, residing in the hills and cemeteries, driving bull, being hunter etc.
However Rudra is an independent God of Rig Veda among others. We find the following information on Rudra in Rig Veda and related literature.
a. Vedic Rudra is as handsome as the supreme Vedic God Indra, having golden complexion. He wears golden necklace and holds golden axe. He helps Vedic people in finding lost cattle.
b. In some Rig Vedic descriptions Rudra is said to be an older than oldest.
c. Rudra’s father is Prajapati. (Maitrayani Sanhita, 6:1-9). In a mythical story Rudra is said to have killed his father, Prajapati.
d. Main epithet of Rudra is “Agni” (Fire).
e. In Agnichayana (a kind of fire sacrifice) to keep the fire kindled, butter is constantly poured in the fire pit, while chanting “Shatarudriya” (Hymns addressed to Rudra) requesting him to immerse in the fire.
f. Rudra is not a single entity but is enumerated from 11 to 60 in different texts of Vedic literature. In this way Rudra represents a group of deities bearing same name. He also is often called the father of Maruts, another group of Vedic Gods.
g. Rudrasavarni, 12th Manu, is said to be son of the Rudra.
h. Taittiriya Samhita states that the sacrifice conducted in the favor of Rudra enriches the host like Indra.
i. There are only three verses dedicated to Rudra in Rig Veda. In a way Rudra was a minor god of the Vedic people.
j. Rudra is depicted as destroyer of humankind and animal in Rig Veda. (RV 2.33.10)
k. Dogs and Wolves are the pets of Rudra. (Atharva veda 11.2.2)
Looking at the above description and myths surrounding Vedic Rudra they nowhere match with the Shiva. Shiva was and is a supreme God for the Non-Vedic people. Shiva is ajanma, having no birth or father. Indeed Shiva is a concept of creation, preservation and destruction of the universe that is worshiped in phallic form. He has no son directly born to him, though kartikeya and Ganesha are associated with him as his sons in later times. Shiva’s mythical abode is mount Kailasa. None of the mythologies associated with him match with of the Rudra’s. Rather Shiva is called "Smarari", destroyer of the fire sacrifices, while all Vedic rituals dedicated to Rudra are associated with fire sacrifices.
Moreover, unlike Rudra, Shiva is worshiped in phallic form. Bharatiy Sanskriti Kosh says in this regards,
“Shaiva religion’s some remnants are not found in the Vedic Rudra’s worship. The most important of it is Shiva is worshiped in phallic form. Phallic worship is practiced in the world from ancient times. Still why only Shiva is worshiped in phallic form? Vedic Rudra was frightful and destroyer whereas Shiva of the non-Aryans was creator and most benevolent. By the non-Aryan He was associated with the fertility and creativity of the land. To them Shiva was creator, preserver and destroyer of the universe. To symbolize his creative powers what else better emblem they could envision than phallic one? (Vol. 9, page 308-9)
From above it is clear that historically both the Gods were different. They represent entirely opposite religions. Yet Shiva was tried to associate with Rudra because it served a purpose of the Vedic people. Under the pretext ofRudrabhisheka (Consecration of Shiva by chanting Rudradhyaya, which originally is meant for fire sacrifice.) Vedic priests earn handsome fees even today.
However, both the gods represent different religions with independent characteristics and myths. Though it seems that Vedic and Non-Vedic religions had been assimilated to form the modern Hinduism, the fact remains that still both the distinct religious streams are flowing parallel to each other. There was no noble purpose behind unifying both the different gods but had selfish interests of the Vedic priests. Had it been out of assimilation of both the religions it would have been welcome step. But keeping independent existence of Vedic religion, hijacking the non-Vedic Gods in a deceitful manner is something that one must think of!