Indeed, the two concepts are different. Compliance check if a specific request was addressed, the conformity check the degree in which a result satisfy the initial request. You can find a related approach in the attached file.

In the context of process mining conformance analyses refers to identifying the gap between a to-be-state and actual as-is-operations. The to-be-state is the (descriptive or normative) process model, the actual as-is-operations are represented by the event log of the real completed process.

Contrarily, compliance checking in the context of process mining refers to testing key controls such as segregation of duties or four-eyes principle. This enables you to compare actual practices against the practices called for in law, policies, standards etc. Unfortunately, both terms are often used interchangeably.

Hi,

The conformance checking there has to be an initial or identified model..the Process mining can be seen in the broader context of Business Process.

Hi Alexey,

Conformance refers to the issue whether principles are garanteed . Compliance on the other side of the spectrum has as point of attention whether the rules are followed as specified i.e. warranted. Applied to the area of process mining as a means to an end it depends on the goal je have in mind and the processmodel you want to test.

Kind regards thanks for your question

Rob

By the way, you can look in here:

Conference Paper Process Mining Manifesto

This paper is well cited and offers a conceptual clarity to which you can refer.