As I learned grammar, neither one of these sentences would be called a run-on sentence. The second sentence is one I refer to as a comma splice, which is an attempt to glue two sentences together with a comma. A comma alone is glue that cannot make two statements stick together. You can use a comma and a conjunction, a semi-colon, or begin a new sentence to fix a comma splice. Here are some examples for you:
I love to bake, apple pie is my specialty. (comma splice)
To fix the comma splice:
I love to bake, and apple pie is my specialty.
I love to bake; apple pie is my specialty.
I love to bake. Apple pie is my specialty.
You might want to check with your teacher to clarify what he or she considers a run-on or a comma splice. It is clear that different teachers can have different ideas about this.
Good luck to you!