This blog provides a high level overview of the differences in connectivity to Ariba network from S/4HANA On-premise and Cloud systems.
In an On-premise environment, most of the configuration and interfaces (IDocs and BAPI) are configured in the back end system, which can be maintained at customer end.
However, in a Cloud environment there is no access to the back-end system. You can get more information on the standard scenarios for connectivity from best practice content and API hub.

Here is the best practice content link : rapid.sap.com/

Ariba Network makes it easy for buyers and suppliers to collaborate on transactions, strengthen their relationships, and discover new business opportunities. Buyers can manage the entire procurement process from source to settle, while controlling spending, finding new sources of savings, and building a healthy, ethical supply chain. Suppliers can help buyers achieve their procurement transformation goals, while boosting customer satisfaction, simplifying the sales cycle, and improving cash flow. Integration of Ariba with S/4HANA takes care of complete end to end processing of various procurement operations.

S/4HANA On-Premise and Cloud are integrated using different methodologies.

On-Premise:

On-Premise follows the process of connectivity to Ariba similar to ECC system, using BAPI(Business Application Programming Interface) calls or through IDoc(Intermediate Document).

BAPI

BAPI is a standard interface to the business object models in SAP products. BAPIs are the primary method through which customer code and third-party applications interact with SAP products.

BAPI are used between SAP (ABAP) apps and with non-SAP applications. BAPIs use RFC-enabled SAP function modules for connectivity, and they are available for master data and transactional data. The communication is Synchronous.

BAPIs are called through RFC calls from Ariba network. :

Example – Creation of a Purchase Requisition through BAPI call BAPI_PR_CREATE, the BAPI is called through Proxy class triggered by Ariba.

 IDoc (ALE Interface)

IDoc (Intermediate Document), is an SAP document format for transferring data among SAP and non-SAP applications. IDocs are available for master data and transactional data and they use XML representation. Useful for asynchronous messaging across firewalls in distributed landscapes.

IDocs transfer from SAP to non-SAP system is done via EDI (Electronic Data Interchange) subsystems whereas for transfer between two SAP systems, ALE(Application Link Enabling ) is used.

IDocs are triggered as HTTP messages from Ariba network and interact with SAP:

Example : IDoc with basic type ARBCIG_ORDERS is used to trigger PO creation .

New world (Cloud integration):

For S/4HANA Cloud connectivity with Ariba , the Communication Arrangements are to be setup in Communication Management of S/4HANA system.  The key features to be understood to setup a Communication arrangement.

Here is the reference blog on communication user: Understanding Communication user in Ariba integration with S4HANA (1ZM,42K)

The connectivity in cloud happens via various services (OData and SOAP) configured in communication arrangements.

SAP API Business Hub( https://api.sap.com/ ) can be used to search or identify the necessary service for the desired requirement, below example screenshots are from API Business Hub.

OData

Open Data Protocol (OData) is a data access protocol, used to query and update data and to trigger business logic. They provide standard CRUD operations via HTTP(S) and are processed Synchronously.

In Scenarios like 1ZM ,2NV ‘API_PURCHASEREQ_PROCESS_SRV’ OData service is used to create and maintain the Purchase Requisition from Ariba network.

SOAP

Simple Object Access Protocol (SOAP) is a protocol for exchanging information in distributed environments and the preferred protocol for asynchronous messaging (error handling).

In scenarios such as 1ZM ,2NV the service  ‘MMPUR_PurchaseOrderRequest_In’ is used to Create,Change and Delete  the Purchase order from Ariba Network.

Hence the communication with Ariba or other external systems in a S/4HANA cloud environment is completely different from On-Premise.