Why is it important recognize the distinction of the roles of "head of state" and "head of government?"

There is a very distinct difference between a head of
state and a head of government. The head of government generally oversees the actions of
a "cabinet," as is the case with the Prime Minister with the Parliament in England. In
this case there is a non-executive head of
state, but that person (Elizabeth II) does not exert the power that
the Parliament does. This has not always been the case, as seen with English monarchs.
Until Charles I was unseated and executed in the 1600s, the monarch always held the
supreme power within the government. At this time—1649—when the Protectorate was formed
and there was no longer a monarch, the power came into the hands of Parliament, and it
has been so since. Even when Charles II returned from exile to take the throne,
Parliament held onto its power, and monarchs had...

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...limited executive
authority.

This is a very
different situation as compared to the executive head of state who
is...

...a
chief public
representative...

The head of
state does not always have the title of "president," however, where the Americas are
concerned, there is a president who is the head of state: this is
called the "presidential system." In some instances, a head of state may be someone who
has assumed power in a non-democratic way, as is the case with dictators. However, the
head of state has executive power and is separate from the legislative branch of the
government. However...

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Presidential governments make no distinction
between the positions of  head of state and head of government, both of which are held
by the president.

Therefore,
my understanding is that the head of government is a person who
oversees a cabinet—this cabinet makes the decisions under the
guidance of the head of government—who has no executive power.
Whereas a head of state is...

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...any head of state who actually governs and is
independent of the
legislature.

The power rests
in two very different places with these distinctive types of leadership. The head of
government does not rule independently, while the "executive" head of state does. It is
important to make this distinction in order to understand who is actually responsible
for leading a country: based on the political hierarchy in place within a certain
country.

Additional
Sources:

http://en.wikipedia.org/wiki/Parliament_of_England

http://en.wikipedia.org/wiki/Charles_I_of_England