In Texas if you're driving with a learners permit and are alone or have no licensed driver with you that is at least 21 years or older then you'll get arrested and have the vehicle towed and impounded.
In Texas if you have a learners permit then you must also have a licensed driver with you that is at least 21 years of age or older and the same is true for most other states.
Getting pulled over with a drivers or learners permit is the same as getting pulled over with a regular drivers license.
However with a learners permit you are usually required to have a licensed driver alongside you who is at least 21 years old or older.
If not then you usually get a fine and may get the vehicle towed.
If you get pulled over with just a learners permit and nobody else is in the vehicle with you such as a licensed driver 21 years or older then you could get ticketed.
In most places the law requires that a driver with a learners permit have a licensed driver 21 years of age or older riding along with them.
If you do get pulled over without that driver and you're under 21 yourself then you might get your vehicle towed or get a warning depending on the laws in your state and officers mood.
But if you just got pulled over for something minor and you have a licensed driver with you then the same thing will happen when you have a regular drivers license.
You just show the officer your learners permit, insurance and registration and then the officer will take it from there.
As long as you were not doing something bad then you will be let go unless you're alone and then if you're alone then you'll get arrested.