What Is Science? From Feynman to Sagan to Curie, an Omnibus of Definitions is collected by Maria Popova at Brain Pickings,
and John S Wilkins at Evolving Thoughts has The Knight’s Song, or What is a Theory?
My own take is that a science is any teachable art of making correct testable predictions. With any restriction as to method or attitude being superfluous to the definition (though not without compelling interest in practice).
And I would say that a theory is just any specific process for making such predictions – including explanatory theories (such as “the butler did it”)as predicting the results of further investigation (such as “you will find the money hidden in his room”), and mathematical theories such as analytic function theory or analytic number theory as being respectively the body of techniques of predicting and proving results a specific area or the possible results from application of a specific class of methods.