From a Celonis academy standpoint, I believe standard processes are the ones that have out-of-the-box connectors and apps in the Celonis marketplace. Something like the Purchase-to-Pay process in SAP would be a standard process because it's a common use case and Celonis has several assets to accelerate time to value for that use case.

A custom process would be something where those assets do not exist or where those assets need high degrees of customization. Perhaps your company has some sort of platform developed internally that you want to explore. Celonis won't have connectors, extraction templates, transformation templates, etc. It all needs to be custom built and therefore is considered a "custom process"

Custom Process: A particular process is not standard and designed specifically for a specific organization and department.

In a nutshell in case of Custom process you will not get ready to use assets by Celonis, You need to build them from scratch.