Testing means "Quality Product"
QA means "quality process for a quality product"

Testing: Aim is find bugs in the application.
QA: Aim is avoid bugs in the application

QA is responsible 4 monitoring and improoving entire 
S.D.L.C phasess  nothing but preventing the bug 
testing is finding bug

Testing examining the behaviour of the application by 
executing on sample data sets

For simple understanding..... QA stands for Prevention and 
Testing Stands for Check up.

QA is nothing but verification.where in focus is giving on 
prevention of bugs. Testing is validation where in focus is 
given on dectecting bugs.QA and testing have a very 
important role in software development life cycle.

To make it more clear here is one example

Assume if a boy studying in 1 std have a aim to be doctor.

then one should make sure. The boy passes all the exams 
from 1 to 10. while taking up 11 he should make sure to 
take up science rather than arts,commerce. Once this is 
done make sure he passes his 12th with good number of marks 
and is qualified for entrance exam.finally when he gets 
this degress in M.B.B.S . He is a doctor.
Watch. the whole process from 1 to his getting M.B.B.S 
degress is nothing but QA that is quality asssurance.

Once the boy is doctor is nothing but Testing. here u r 
testing wheather the boy is doctor or not. It is as good as 
saying wheather he passed or failed.

In Short 
QA: Prevention of errors

Testing: detection of errors.

In detail

QA is the process to ensure that all the procedures and 
standereds are establish and followed throughout the life 
cycle.

Testing is the process to execute the system in both 
Favorable and unfavorable conditions in order to find the 
bugs.

In favorable conditions it produced the correct results and 
in unavorable conditions it produced the correct results.

QA is prevention of introduction of defects
where as testing is detection of defects in products and 
services

QA - A set of activities designed to ensure that the 
development or maintenance process is adequate to ensure 
that the system meets the objective

Testing - Executing the system with the intend of finding 
defects.

(QC - A set of activities designed to evaluate a developed 
product)