NO its not same

Retesting:

Re executing the same test case again and again is 
retesting.(For example once the bug is fix from the 
developer, after that for the varification purpose we need 
to re execute the same test case know that is retesting.)

Regression testing:

Regression testing is nothing but once the bug is fixed we 
need to test wheather the that fix can make anyother 
problem elsewhere.

retesting means  reexcuation of test with mulitipletest 
data to valiadte this function is called retesting.

regression means in any application new functionalities can 
be added so the application has to be test to see whether 
added functionalities are affected to the exiciting 
funcunalites or not

no regression testing and retesting are different
Regression testing means testing the already functionality 
in two different sinerios
1.when the test engineer finds the bug and post it to the 
doveloper the doveloper rectifies them and send it to the 
testing department, the test engineer once again test all 
the module testing by him because if any modifications are 
done by the doveloper and due to these changes whether his 
application is effected or not
2.whenever any new changes are made by the doveloper the 
test engineer once again test all the application tested by 
him to confirm that his application is safe.

Retesting means testing the already tested functionality by 
using different sets of values to rule out environmental 
issues

retesting &regresion testing is not same.
retesting is testing the same build.
regresion testing is testing the modified build.