Difference between EXISTS and IN in SQL?

Question

What is the difference between the EXISTS and IN clause in SQL?

When should we use EXISTS, and when should we use IN

Answer 1

IN supports only equality relations (or inequality when preceded by NOT).
It is a synonym to =any / =some, e.g

select    * 
from      t1 
where     x in (select x from t2)
;

EXISTS supports variant types of relations, that cannot be expressed using IN, e.g. -

select    * 
from      t1 
where     exists (select    null 
                  from      t2 
                  where     t2.x=t1.x 
                        and t2.y>t1.y 
                        and t2.z like '℅' || t1.z || '℅'
                  )
;

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And on a different note -

The allegedly performance and technical differences between EXISTS and IN may result from specific vendor's implementations/limitations/bugs, but many times they are nothing but myths created due to lack of understanding of the databases internals.

The tables' definition, statistics' accuracy, database configuration and optimizer's version have all impact on the execution plan and therefore on the performance metrics.