A VSG, which is also known in the literature as a synchroverter, as you mentioned, is an endeavor to emulate the dynamics of a synchronous generator, through an elaborate inverter. If you implement the VSG control scheme onto your inverter, then you can also apply vector control that is usually encountered when controlling generators, including droop control to achieve power sharing in a regulated manner, for example. Therefore, it is obvious that a VSG is a control scheme while droop control is a control methodology. In any case, the "Inertia" in the case of the VSG is as you stated 'virtual'. Main reason for this is the fact that in order for the inverter to properly operate as a VSG it requires a constant DC voltage source in its input which is not affected by disturbances. In practice though this condition cannot be easily fulfilled since in a PV source based installation, if a cloud covers the PV panels, then the dc voltages that feeds the inverter will instantly diminish to 0. In this case the inverter cannot showcases any signs of resilience or inertia. Another case would be to connect a load with needs higher than the capabilities of the inverter. Again you would witness a similar result.

Actually, both these two control strategies aim at mimicking rotor characteristics of synchronous generators (SGs). To be specific, traditional Droop control is devised based on the steady-state droop characteristics of SGs, while VSG control further emulates swing equations of SGs.

The differences between them can be enumerated as 1) Droop control can provide inertia yet VSG control can't, 2) transfer function (active power control loop) of the Droop control is a first-order system but that of the VSG control is a second-order system, and thus VSG control may result in power fluctuations in some cases.

Note that, the above Droop control only corresponds to the traditional Droop control, for some improved Droop control schemes, e.g., LPF-based Droop control, this type of control can also provide inertia and the transfer function alter into a second-order system.

I also provide a theoretical deduction in the attached. I hope it'll help you.

Droop control and virtual synchronous generator (VSG) are two different control strategies used in inverter-based resources, such as renewable energy sources like solar or wind power systems. While they both aim to achieve grid synchronization and stability, they employ different approaches to achieve these goals. Here's an overview of the differences between droop control and a virtual synchronous generator:

1. Control Strategy:

• Droop Control: Droop control is a decentralized control strategy that mimics the behavior of traditional synchronous generators. It uses a frequency droop characteristic, where the output frequency of the inverter is inversely proportional to the active power (or frequency deviation). This means that as the load increases, the inverter reduces its frequency to maintain power balance.
• Virtual Synchronous Generator (VSG): VSG control, on the other hand, is a centralized control strategy that emulates the behavior of a synchronous generator virtually. It aims to provide the same grid-supporting characteristics as a synchronous generator, including inertial response and voltage regulation. VSG control achieves this by utilizing feedback control loops and advanced control algorithms.

2. Operation Mode:

• Droop Control: In droop control, the inverter operates in a voltage control mode. It adjusts its output voltage magnitude based on the active and reactive power demand from the grid. The frequency of the inverter is controlled by the droop characteristic.
• Virtual Synchronous Generator: In VSG control, the inverter operates in a current control mode. It actively regulates the current injected into the grid to mimic the behavior of a synchronous generator. This control mode enables the VSG to provide better grid stability and support, including fault ride-through capability.

3. Response to Grid Events:

• Droop Control: Droop-controlled inverters have limited grid support capabilities during transient grid events, such as faults or disturbances. They primarily rely on the droop characteristic to adjust the frequency and maintain power balance, but they may not provide active fault management or dynamic voltage support.
• Virtual Synchronous Generator: VSG-controlled inverters are designed to respond more actively to grid events. They can provide inertia emulation, allowing them to simulate the inertial response of synchronous generators. VSGs also offer more advanced grid support functionalities, including active power control during grid faults and voltage regulation to support grid voltage stability.

4. Flexibility:

• Droop Control: Droop control is relatively simpler to implement and widely used in many grid-connected renewable energy systems. It offers good stability and synchronization characteristics, but it may lack some advanced grid support capabilities.
• Virtual Synchronous Generator: VSG control is more complex and requires advanced control algorithms to emulate synchronous generator behavior. It provides enhanced grid support functionalities, making it suitable for applications where grid stability and support are critical.

In summary, droop control and virtual synchronous generator are two distinct control strategies used in inverter-based resources. Droop control relies on a decentralized frequency droop characteristic, while VSG control emulates the behavior of synchronous generators using centralized control algorithms. VSG control provides more advanced grid support capabilities, including fault ride-through and voltage regulation, but it is also more complex to implement compared to droop control.