Is there a difference in meaning between będę spać and będę spał?
In terms of meaning, they are the same. A man can say both "będę spał" and "będę spać" and a woman can say "będę spała" and "będę spać". It's just that one version shows the gender and the other does not, which can be important in some contexts.
feminine version is one syllable longer, which is why women are more likely to use "infinitive version", especially if a verb is longer and infinitive is not a tongue twister.