There are many differences, here I will mention what I deem to be the most important:
Presidential :1) In a Presidential System the President is both Head of State and Head of Government. Presidents under this system almost always have the most power. 2) In a Presidential System there is a (more often than not) complete separation of powers. 3)The President usually relies on a popular mandate (elections) and not the confidence of the legislature to gain and/or hold onto power. 4) Legislative terms are fixed, a legislature in a Presidential system can't be dissolved
Parliamentary: 1) In a Parliamentary system there is a complete separation btwn the Head of State (Monarch or President) and the Head of Government (Prime Minister or Chancellor) . 2) In a Parliamentary system the Head of Government usually holds the most power the Head of State may hold some emergency powers and also gives laws the final approval. 3) Separation of powers are blurred in Parliamentary systems (example: The Govt of the UK is formed of members of parliament) 4) The Government must hold the confidence of the legislature to continue its mandate of governing (simply put the Prime Ministers party or coalition must hold a majority in the legislature). 5) Parliamentary systems do not have a fixed term usually only a maximum number of years, if the legislature finds no confidence of the government of the day then the legislature may be dissolved and new elections held)
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In the US Presidential system the President is the executive leader. He is voted by the people or by elected body directly. Where as in the Parliamentary system the legislative branch elects the Prime Minister and if the Parliament can cast a vote of no confidence and replace him if they do not like him.
Both allow citizens to vote for members of the legislature
This question doesn't really belong in the US-related sections; since the US uses a presidential rather than a parliamentary system, parties don't "form a government." In a parliamentary system like the one in the UK, when two parties cooperate it's known as a coalition government.
Do the voters elect electors not the presidential candidates
it's Parliamentary democracy and Constitutional monarchy
In US politics, being an early front-runner in a US presidential campaign guarantees you will be in the first Presidential Debate. This also brings more media coverage, but it does not guarantee you would be the party's nominee.