Persistence means trying repeatedly to reach a goal through the same method, figuring eventually you'll succeed. Tenacity means trying to reach a goal through varying methods, learning from each failure and trying different approaches. For anyone striving to achieve a goal, tenacity may be the better approach.

I have a friend (and editing client) who used to be a pantser. But she found that after finishing every draft, she had so many loose ends to address and problems to fix, it took her much longer to revise than she'd like. So she started forcing herself to plot before she began writing each book. Not detailed outlines, but she figures out who kills whom, how, and why, what her subplot will be (again, just the basics), and what her theme is. These changes in her approach have enabled her to be so much more productive. She writes faster now, and she needs less time for revision. That's tenacity in action.
Moving on to a finished product, how do you react to rejection? If you have a rejected short story, for instance, after you curse the universe, do you find another venue and send that story out immediately? Or do you reread it and look for ways to improve it? If a story has been rejected several times (there's no shame here; we've all been there), do you keep sending it out anyway or do you put it in a drawer to let it cool off for a few months or until the market has changed or your skills have improved?
If sending a story out a few times without revising after each rejection usually results in a sale for you, great. Then your persistence works, and it means you have more time for other projects. But if you find yourself sending a story out a dozen times without success, then perhaps you should consider a new approach. After a story is rejected, say, three times, maybe you should give it a hard look and see how it can be changed. Maybe you should let it sit in a drawer for a while so when you review it, you'll have a fresh take.
And if you're getting a lot of rejections, perhaps it's time to re-evaluate your markets or what you write. I know some writers who started their careers writing science fiction, but it turned out that they were better suited to writing mysteries. Once they let their true selves out on the page, they started making sales. I know a writer who's been working on a novel for years, but she can't seem to finish it. Yet she's had a lot of success with short stories. If she were to decide to only write short stories and let the novel lie fallow, that wouldn't be a failure; it would be tenacity in action: finding what works for her.

But if you believe writing is the right fit, yet you aren't as productive as you'd like, or your sales aren't as good as you want them to be, then be tenacious. Evaluate your approaches to getting writing done, to editing your work, to seeking publication.
That, my fellow writers, is my advice for you. Be tenacious. Evaluate what you want, and evaluate your methods for getting there. If your methods aren't working, change them. If in six months your new methods aren't working, change them again. Work hard. Work smart. And be sure to enjoy yourself along the way, because if you're not enjoying writing, why bother doing it?
And now a friendly reminder: I'm honored to have two short stories nominated this year for the Agatha Award, "A Matter of Trust" from the anthology Three Strikes--You're Dead! and "The Postman Always Flirts Twice" from the anthology Agatha and Derringer Get Cozy. They, as well as the three other Agatha-nominated stories, can be read online for free. Click here to go to the Malice Domestic website and scroll down to the short story titles. Each one is a link to a pdf of that story.