Your summary is correct! Here’s a more detailed breakdown of the SUI token’s role, based on the official Sui documentation:

What is the role of the SUI token?

The SUI token is the native asset of the Sui blockchain and serves four main purposes:

1. Staking:

   • SUI can be staked to participate in the proof-of-stake mechanism.
   • Token holders can delegate their SUI to validators to help secure the network and earn staking rewards.

2. Paying Gas Fees:

   • SUI is required to pay for transaction execution and storage on the Sui network.

3. Governance:

   • SUI holders have the right to participate in on-chain governance, such as voting on protocol upgrades.

4. Versatile Asset / Collateral:

   • SUI acts as a liquid asset for various applications, including as a unit of account, medium of exchange, store of value, and as collateral in DeFi protocols.

“The SUI coin serves four purposes on the Sui network:

• You can stake SUI to participate in the proof-of-stake mechanism.
• SUI is the asset denomination needed to pay the gas fees required to execute and store transactions or other operations on the Sui network.
• You can use SUI as a versatile and liquid asset for various applications, including the standard features of money... and more complex functionality smart contracts enable, interoperability, and composability across the Sui ecosystem.
• SUI coins play an important role in governance by acting as a right to participate in on-chain voting on issues such as protocol upgrades.”

— Sui Tokenomics Documentation

The SUI token plays a key role in the Sui blockchain by letting you pay for gas fees when making transactions or interacting with smart contracts. You also use it to take part in staking, which helps secure the network and earn rewards. If you're a validator, you receive SUI as compensation for processing transactions and keeping the system running. The token is also used in governance, so you can vote on updates or changes to how the blockchain works. This makes SUI essential for both day-to-day operations and long-term development of the network.

You can read more about the SUI token and its uses here: https://docs.sui.io/learn/sui-token