A sentence fragment is a group of words that is not
a main clause, but it has been punctuated as though it
were:
When I have finished my homework.
The above group of words has a capital and a period, so
it is pretending to be a complete sentence, but it is
only a subordinate clause. In dialogue, this fragment
might be punctuated as a sentence if someone is portrayed
as responding to a question like, "When can we go for a walk?"
In other cases, it should be attached to a main clause and
set off with a comma.
A comma splice consists of two main clauses which
are not punctuated as such:
They drove to Ottawa, they looked for a parking place.
This apparent single sentence contains two main clauses
attached to each other with nothing more than a comma. A
comma just doesn't have enough power to "splice" or "join"
two main clauses by itself. You need a coordinate
conjunction, or you might turn one of the main clauses
into a free modifier, like this:
After driving to Ottawa, they looked for a parking
place.
A run-on sentence is a comma splice without the
comma. Fix it the same way you would fix a comma splice.