def METHOD_NAME(first, other):
    """Loosely check whether or not the Woodwork schemas are equivalent. This only checks that the string values for the schemas are equal and doesn't take the actual type objects into account.
    Args:
        first (ww.Schema): The schema of the first woodwork datatable
        other (ww.Schema): The schema of the second woodwork datatable
    Returns:
        bool: Whether or not the two schemas are equal
    """
    if first.types.index.tolist() != other.types.index.tolist():
        return False
    logical = [
        x if x != "Integer" else "Double"
        for x in first.types["Logical Type"].astype(str).tolist()
    ] == [
        x if x != "Integer" else "Double"
        for x in other.types["Logical Type"].astype(str).tolist()
    ]
    semantic = first.semantic_tags == other.semantic_tags
    return logical and semantic