Your question basically refers to the modeling of processes, in your case service processes. Process modeling usually solves this methodically by hierarchizing processes into subprocesses and, if necessary, into activities. What can be regarded as a process or sub-process depends on the perspective, i.e. on the question on which the process modeling is based. Thus on a rough level a service process can be part of a superior customer process, or it can be an independent process, which is to be subdivided further.

Descriptions and discussions on this topic are easy to find. e.g. https://www.processmodel.com/learning-center/users-guide/chapter-7/

Understanding the service process is essential to provide good customer service. The customer service process is refers to the group of activities that we carry out from the moment we receive the first contact from a user until we solve his or her problem and we say goodbye to the customer.

A Sub-process is a separate process that is embedded in another process. It is a process that is part of a larger process.

Actually your question is a little bit broad without clear context. still i think as far as i understand any business process comprised of two aspects one is provider aspects where in literature its termed as service blue print i.e. how the service is designed and provided to consumer while other aspect is consumer side i.e. how consumer or actually a recepient of service perceives and experience the service mostly called in literature by name of service scripts. there has to be a match among both of them for mutual co-creation or benefit of stakeholders especially provider and consumer. Subprocess is merely individual elements of complete process specifying how service script is going to be aligned with service blue print. There is also a discussion in literature on how service and services are distinguised (means singular and plural terms). plural term refer to marketing of business which are by nature actually a services business while service in singular form is talking about underlying logic of service in every form of busness irrespectie of product oriented or service oriented firms. actually authors recently started claiming that even product buisness are rooted in service means when you buy car you actually dont buy car (product) but you buy transportation service. For further details read Christopher and Lovelook book on services marketing

Clearly defining your stakeholders role and responsibilities is a starting point to create the process map that includes the service processes and sub-processes. Understanding timing and interaction/accountability of processes with sub-processes will be needed to create the process flow chart which would contain decision tree responses. For more information on creating process flow charts: https://www.businessport.net/benefits-swim-lane-process-maps-diagram/