I often wonder why people ask these kinds of questions rather than take a moment and with minimal effort open a dictionary or thesauraus.
Let's give it a whirl, shall we?
They can have similar usage and meanings in different forms and contexts, but each are distinctly unique words.
I can say about this "let's give it a whirl" and that makes sense, but if I said let's give it a "swirl" -- well, that would be babbling nonsense.
By the way, the saying, "let's give it a whirl" means to try it out, give it a try, a test, etc.
Give it a swirl would mean give a stir or a pattern of spirals, not the same as "give it a whirl" -- an example
of difference in context.
Now, just because I'm who I am, let me throw this at you.
What about "whorl" and "swirl" and "whirl" ...???
An answer is right at your fingertips...
...and even more so if your fingertips are on the pages
of your dictionary.
I'll go ahead and cheat for you -- in both noun and verb forms, "whirl," "whorl" and "swirl" all carry the same basic meanings -- to gyrate or spin (verb) or the act of doing so (noun). They have other uses and contexts, but you can use those littles whorls/swirls/whirls on your fingertips to grapple with the pages of your dictionary.
Now, I must whorl away, pardon the swirl I leave behind in my wake, as the whirlwind rushes in to fill the vacuum my sudden departure has made.