Is it okay for an author to create two different stories that share the same motif? That is, if they explore the concept differently?

Absolutely, holy crap. Some writers have only one theme they explore their entire lives, that’s fine.

I have three themes I explore a lot, they appear over and over in my work.

1) The Search For Identity. Many of my characters have lost their identity, or had it taken/altered, or are otherwise bereft of a sense of self or history. They are trying to get it back. This resonates with me forever, I know it means a great deal to many people trying to answer they basic question of who they truly are.

2) The Search For Family. Very few of us had a Brady household. Many of us have different meanings for the words, “father,” “mother,” or “sibling,” for example. I write a great many stories about being able to forgive, or at least move on, from that, and a fair number about NOT feeling pressured to forgive when the offense is egregious. But in the end, many of those same stories end up being about characters finding family later in life, in unexpected places.

and

3) The Will To Survive. This is a big one to me. I get a lot of questions about, “Why do you write such dark scenarios” and “why do you put your characters through such hell” and the answer is simple, because real people go through Hell every day. Real people suffer from crime, injury, illness, neglect, poverty, addiction, abuse, prejudice and an untold number of other maladies. I like to tell stories of people surviving. I don’t care much about two superheroes fighting over a golden piece of crap, or a hero stopping a bank robbery. Those can be fun, but they don’t really move me. 

My thing is, my characters have horrid things happen, but they survive. I feel like sometimes, just surviving is INCREDIBLY heroic. When I hear readers tell me of the things that they have had to deal with in their lives, I don’t feel motivated to write a story where Superman stops a jewel heist, I feel motivated to write a story where someone finds a way to open the windows again when all they want to do is leave them closed. I feel like seeing characters try to outlive their traumas, however they choose to do it, is very meaningful to me as a reader, and I hope as a writer. 

It’s another case of being inspired by the readership, and it informs almost all my writing in some way. It’s also why I wrote Deadpool as a troubled guy who tells jokes, rather than as Bugs Bunny with a gun. I think you can laugh at zany Deadpool, but there’s so much more to the character than just that.

Anyway, those themes show up again and again in almost all my books. Write what moves you, it’s hard for others to truly care if the author doesn’t.