Two sample independent t test?

Let me give you an examples.

Let's say you develop a new computer software to help people sharpen their typing skills.

You have 60 volunteers to test the software.
_______________________________________________________________
So you design an experiment.

You randomly assign 30 to try the new software, and 30 to try the old software.

Then you want compare the mean between both of the samples. Here you would use two-sample independent t-test. Both sample were independent of another.
_______________________________________________
Now you can also do an alternative experiment.

Test the 60 volunteers speed before trying the new software.

Then have them try the new software and test their speed afterward.

Now you would use a matched pairs t-test. (not independence)
_______________________________________________
I hope this helps you understand.