Why did India end up tilting" to the Soviet pole during the Cold Wars, while Pakistan was pro- US pole? And to what degree was India pro Soviet?
India never joined the Soviet pole or the Soviet bloc though India and the Soviet Union (USSR) enjoyed a strong strategic, military, economic and diplomatic relationship.
After independence both India and Pakistan were backward and needed support from stronger nations. Pakistan joined the Western bloc by signing SEATO and CENTO. India developed closed ties with Soviet but remained Non-Aligned in the Cold War.
The reasons for strong Indo-Soviet ties despite NAM:
Western bloc (US bloc) was dominated by colonialist and imperialist nations. In 1947 India was just freed from colonialist and imperialist British. India's one of the most important objective in the international sphere was to fight against colonialism and imperialism, protect its own and other newly independent nations' sovereignty. These principles also features in NAM.
India faced deliberate estrangement from the West during the Kashmir Issue at the UN. West supported Pakistan on this.
Most of the Indian leaders had socialist leanings. Some mainstream leaders, like M. N. Roy, were good friends of the Stalin. Pundit Nehru, India's first Prime Minister, also shared good relations with Stalin and Khrushchev. Nehru was very impressed with the Soviet advances in the fields of science and technology.
At the time of independence, India was backward economically, militarily, in food productions and many other fields. She needed support for her development and started taking support from Soviets.
In February 1954, the U.S. administration of President Dwight D. Eisenhower announced the decision to provide arms to Pakistan, followed a month later by Pakistan joining the SEATO and subsequently the CENTO. These agreements assured Pakistan the supply of sophisticated military hardware and economic aid. This alarmed India, which had uncomfortable relations with Pakistan.
China invaded India in 1962. The presence USS Enterprise in the Bay of Bengal during 1971 Bangladesh war was fresh in the mind of Indians. In 1972, Nixon visited China. The repercussions of the Nixon visit were vast, and included a significant shift in the Cold War balance, pitting the PRC with the U.S. against the Soviet Union.
India and the USSR therefore pursued similar policies based on common security threat born out of the US interests in Pakistan and later in China.
India and USSR signed The Indo-Soviet Treaty of Peace, Friendship and Co-operation on 9 August 1971.
The only 'military' related clauses in The Indo-Soviet Treaty of Peace, Friendship and Co-operation treaty are:
(ARTICLE VIII) In accordance with the traditional friendship established between the two countries, each of the High Contracting Parties solemnly declares that it shall not enter into or participate in any military alliance directed against the other Party.Each High Contracting Party undertakes to abstain from any aggression against the other Party and to prevent the use of its territory for the commission of any act which might inflict military damage on the other High Contracting Party.
(ARTICLE X) Each High Contracting Party solemnly declares that it shall not enter into any obligation, secret or public, with one or more States, which is incompatible with this Treaty. Each High Contracting Party further declares that no obligation be entered into, between itself and any other State or States, which might cause military damage to the other Party.
Both of these clauses ultimately relates to peace and non-aggression against each other.
In some of the incidents, India had also shared good relations not only with the USSR but also with United States during the Cold War.
In initial years of independence, due to poor harvest, India asked for free food from US. US made the donations and from 1947–1959 the U.S. provided $1.7 billion in gifts, including $931 million in food.
During the Chinese invasion of 1962, even in the midst of the Cuban Missile Crisis, United States was willing to help India. There were plans to send the USS Kitty Hawk aircraft carrier to the Bay of Bengal to support India.
UPDATE 17th August '13 :
Very recently declassified CIA files shows that Pundit Nehru gave permission to the US to use Indian airbase Charbatia in Orrisa state to spy on China after 1962 conflict. US was also going to use this base for spying on USSR. From today's (17th August '13)The Indian Express
The CIA report, released by the National Security Archive, states that the US had two missions in mind when it stationed aircraft in India — to get a clear picture of Chinese deployment along the disputed border and to use it as a staging area to spy on the Russian anti-ballistic missile (ABM) testing site at Saryshagan (now in Kazakhstan).
So, India did not actually join the Soviet Bloc or US Bloc. As also there was no formal agreement like NATO, CENTO, SEATO or Warsaw signed by India unlike what the Pakistan did. India was just pursing its national interests, without compromising its Non-Alignment principles, with more inclinations towards Soviets than the US.
India didn't "officially" join the Soviet bloc in the sense of being a signatory to the Warsaw Pact in Eastern Europe.
India DID unofficially "align" with the Soviet Union in Asia.
This was to create a counterweight to the Chinese-Pakistani "understanding" that originated in 1962 over the Kashmir (China invaded India on Pakistan's behalf). The need for some sort of "understanding" with the Soviet Union grew further as a result of the U.S. rapprochements with Pakistan, and with China, in 1972.
India was "socialist" and therefore somewhat ideologically compatible with the Soviet Union. But mainly it was a case of "the enemy of my enemy is my friend." They actually had few interests in common to be truly "allied."