Process mining is a discipline that lies at the intersection of data science and process management. It focuses on analyzing business processes based on event logs to extract insights, monitor conformance, and improve processes. Within process mining, there are primarily three main areas of focus: process discovery, conformance checking, and process enhancement. Each has its objectives and methodologies, and I'll explain how they differ from each other, particularly focusing on the concept of process enhancement.

### Process Discovery
Process discovery is the first step in process centric analysis. It involves using data from event logs to create a process model without using any a-priori information about the process. This is essentially about discovering the workflow or process map by identifying the events (actions) reported in the logs, such as the order in which tasks are processed and the pathways taken through a system. The resulting model (often depicted as a BPMN diagram or a Petri net) provides a visualization of the process as it actually occurs.

### Conformance Checking
Conformance checking comes after a process model is discovered or proposed. This step involves comparing the event log data, the 'actual behavior,' with the designed process model, 'the expected behavior,' to identify discrepancies. These discrepancies can be violations of the expected sequence of tasks, missed activities, or activities executed out of the expected order. The primary goal of conference checking is to assess if the actual operational processes conform to the supposed rules or standards and to highlight deviations along with non-compliance.

### Process Enhancement
Process enhancement, also known as process improvement or extension, is aimed at improving the existing process based on insights derived from process discovery and conformance checking. It moves beyond just understanding what the process is or whether it aligns with a pre-defined model. Instead, it focuses on optimizing process performance.

#### What Contributes to Process Enhancement:
1. **Adding Perspective**: It can involve augmenting the current process model with additional perspectives such as time, cost, and quality. For instance, analyzing process logs to find bottlenecks or inefficiencies such as long waiting times or repeated tasks. 

2. **Modifying Process Pathways**: Based on the insights gathered from the performance and compliance issues identified during discovery and conformance checking, changes can be recommended to eliminate process redundancies, avoid bottlenecks, and reduce waste.

3. **Resource Optimization**: Process enhancement may include better allocation and utilization of resources, reducing downtime, and optimizing task allocation.

4. **Predictive Modelling**: Developing predictive models to anticipate future process outcomes and behaviors based on historical data, contributing to more dynamic adaptation of processes.

5. **Offering Recommendations**: Based on the analysis, specific recommendations for process change can be offered, including the integration of best practices, process re-engineering, or automation of repeated tasks.

### Differences from Process Discovery and Conformance Checking

While process discovery is about identifying what the actual process is and conformance checking about ensuring the process aligns with certain standards or models, process enhancement is inherently about making the analyzed process more efficient and effective. It is proactive, using insights gained from the initial stages (discovery and conformance) to suggest improvements, enhance performance, and contribute to business goals such as cost reduction, faster execution times, and improved service quality. This distinguishes it from the other two areas which are more inclined towards descriptive and diagnostic analysis.