Key Difference: A relationship between both, a successor and a predecessor depends on the type of task dependency to use. A successor is a person who follows and takes the place of another. Whereas, a predecessor is someone who has had a particular job or position before.

Dictionary.com defines ‘Successor’ as, “a person or thing that succeeds or follows” and “a person who succeeds another in an office, position, or the like”. Successor is also a number that follows or just comes after a particular number. A successor takes place of the retired official or the present holder who need to leave or resign.

Examples for successor are:

• Harry is resigning his job. He need to find his successor immediately.
• The Crown Prince will be successor to the throne,
• The CEO's successor used to be the vice president here.
• John succecced Tom's position as Marketing Manager. 
• Successor of 358 is 359.
• Successor of 11 is 12.
• Successor of 2307 is 2308.

On the other hand, dictionary.com defines ‘Predecessor’ as, “a person who precedes another in an office, position, etc.”, "something succeeded or replaced by something else”. The ancestors (forefathers) are also known as predecessors.

Examples of Predecessor are:

• The new monument in the park is more beautiful than its predecessor.
• She was my predecessor as Manager.
• My predecessors came from Canada.

A relationship between both, a successor task and a predecessor task depends on the type of task dependency to use.

• Predecessor: A task whose finish date determines the start date of its successor task.
• Successor: A task whose start date is driven by its predecessor task's finish date.

In a mathematics expression, successor and predecessor are the numbers which come after or before a particular number. On the other hand, in a business or an organization, successor and predecessor are those who take a position or were in that position for a particular time being. 

There’s not so much to describe between the two terms ‘Successor’ and ‘Predecessor’, it very clearly states their responsibility and duty.

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