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In Stellar Laboratory, in the Transaction Builder tab, the Transaction Sequence Number is required, there is button which gets the next Sequence Number.
Does Stellar Laboratory gets the sequence Number information from the stellar-core database?
If it does, how does it query it, and is it in anyway similar to how a thin-client works in Bitcoin?
Stellar Laboratory interacts with Horizon. It sends a request to /accounts/{account} endpoint to retrieve account details (sequence number in this case).
Horizon exposes an API layer for interaction with data stored on the ledger. Moreover, Stellar lab (and all other web-based wallets) submit signed transactions to the Horizon server which then re-sends them directly to Stellar Core.
