Formalism is not structuralism. Unlike formalism, structuralism is more concerned with the context of relationships than with relationships themselves. Why? Because structuralism assumes context constructs or causes or biases relationships.
Formalism does not neglect origin or cause or bias, but assumes, because of common and universal characteristics of forms, that origin and cause and bias are DEEP. That is, formalism assumes that origins and causes and biases of forms are capable of discovery but incapable of immediate manipulation or change. For this reason, formalism seeks LAWS of forms (i. e., laws of abstractions and references — or the science of signs).
Structuralism does not prioritize common and universal characteristics of forms. In most cases, structuralism denies such characteristics exist. On the contrary, structuralism finds that different contexts — most particularly different SOCIAL-CULTURAL contexts — construct fundamentally different forms. Therefore, there is no proper science of signs nor laws of forms. Rather, there is the ongoing study of those social, cultural, and political contexts that construct, manipulate, or otherwise impose forms.
If structuralism were then to assign fundamental form to social, cultural, or political context, then the difference between formalism and structuralism would be slight. But, while structuralism isolates context as fundamental to the structure of form, it finds no fundamental mechanism — at least no fundamental formal mechanism — that typifies context. Subsequently, this tends toward relativism, which is not universally associated with structuralism, but is commonly so.
These questions highlight the major differences between formalism and structuralism as distinct critical positions.
Are forms universal? Formalism says yes. Structuralism says no.
Are forms biological in origin? Formalism says yes. Structuralism says no.
Do forms ultimately reference something else (e. g., culture)? Formalism says no: Forms (particularly game forms) are most fundamentally self-referential and, for that reason, paradoxical and most interesting. Structuralism says yes: Forms ultimately reference material objects or processes; self-referential and paradoxical forms are, therefore, meaningless and not interesting at all.