/lit/ - Literature

Comma splices get brought up a lot here and so I've finally looked up what the term actually means. Can someone let me know if I'm understanding this correctly?
If I have two independent clauses (I'm a bit shaky on the definition of a clause as is) I should separate them with a full stop or a semi-colon:
>Today I went on a long walk. I happened to see a squirrel.
>Today I went on a long walk; I happened to see a squirrel.
So the above two are correct, whereas the following is incorrect:
>Today I went on a long walk, I happened to see a squirrel.
And kind of tangentially, this would be a run-on sentence:
>Today I went on a long walk and I happened to see a squirrel.
Have I misunderstood any of this? And can anyone maybe give me a basic understanding of what a 'clause' actually would be? What specifics makes clauses independent?