What fundamental differences in ideals separated the American colonies from Great Britain after 1763?

Actually, there was not a great deal of difference between
American and British ideals. Almost all Americans prior to the revolution considered
themselves the King's good and loyal servants and were proud of their English heritage.
The most precious of these was their "rights as
Englishmen."

After the Seven Years War when Parliament
attempted to tax the colonies for the expense of defending them, the colonists insisted
that they had been denied their rights as Englishment. Even after Lexington and Concord,
an Olive Branch Petition was sent to George III offering to call off hostilities if they
could only be granted their rights as Englishmen:

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The apprehension of being degraded into a state
of servitude from the preeminent rank of English freemen, while our minds retain the
strongest love of liberty, and clearly foresee the miseries preparing for us and our
posterity, excites emotions in our breasts which, though we cannot describe, we should
not wish to conceal. Feeling as men, and thinking as subjects, in the manner we do,
silence would be disloyalty. By giving this faithful information, we do all in our power
to promote the great objects of your royal cares, the tranquility of your government and
the welfare of your people.

We ask but for peace, liberty,
and safety. We wish not a diminution of the prerogative, nor do we solicit the grant of
any new right in our favor. Your royal authority over us, and our connection with Great
Britain, we shall always carefully and zealously endeavor to support and
maintain.

George III refused
to even read the petition. It was only after this, that Thomas Paine wrote Common sense
in which he argued that the King (and Parliament) were responsible for the war; and that
the Americans had evolved into a separate nation who could no longer be part of the
British Empire:

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Every thing that is right or natural pleads for
separation. The blood of the slain, the weeping voice of nature cries,
'tis time to part. Even the distance at which the
Almighty hath placed England and America, is a strong and natural proof, that the
authority of the one, over the other, was never the design of
Heaven.

There is some
argument that during and after the Seven Years War, Americans developed a separate
identity as such. Still American ideals and British ideals were not that
different.