What is it?
In Software Engineering, a test is an individual process which performs a verification that the software is built accordingly to the Requirements, and a validation of the features, so that they can attend the customer accordingly. In other words, a test checks if all functionality is correctly implemented in all levels of the software.
What are errors?
When talking about testing, some concepts come to surface:
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ErrorDetected difference between the obtained result and the expected result. 
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FaultIncorrect code lines or block that causes an error. 
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FailureSoftware malfunction, possibly caused by an fault. 
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MistakeWhat produces an fault in the software.