Magento2 – How to Get Attributes Based on Attribute Set ID or Name

Since no one answered my question, I tried a bit of workaround and this was what I came up with and actually worked my purpose. Hope it helps for anyone with the same issue later.

public function getSpecificAttributes($product) {
    //to get ids of all the attributes in the default attribute set
    $entityTypeId = Mage::getModel('eav/entity')
            ->setType('catalog_product')
            ->getTypeId();
    $attributeSetName = 'Default';
    $defaultAttributeSetId = Mage::getModel('eav/entity_attribute_set')
            ->getCollection()
            ->setEntityTypeFilter($entityTypeId)
            ->addFieldToFilter('attribute_set_name', $attributeSetName)
            ->getFirstItem()
            ->getAttributeSetId();

    $defaultAttributes = Mage::getModel('catalog/product_attribute_api')->items($defaultAttributeSetId);
    $defaultAttributeCodes = array();
    foreach ($defaultAttributes as $attributes) {
        $defaultAttributeCodes[] = $attributes['code'];
    }

    //get ids of all the attributes in the attribute set specific to the current product
    $attributeSetId = $product->getAttributeSetId();
    $specificAttributes = Mage::getModel('catalog/product_attribute_api')->items($attributeSetId);
    $attributeCodes = array();
    foreach ($specificAttributes as $attributes) {
        $attributeCodes[] = $attributes['code'];
    }

    $currentAttributes = array_diff($attributeCodes, $defaultAttributeCodes);
    return $currentAttributes;
}

You can use the Magento\Eav\Api\AttributeManagementInterface service contract class:

$attributeManagementInterface->getAttributes(\Magento\Catalog\Api\Data\ProductAttributeInterface::ENTITY_TYPE_CODE, $attributeSetId);