Your notes on both machines, no subscription, no cloud copy.
Keep the vault on one machine (say, the desktop) and share it. On the laptop, open the vault from the shared folder: Obsidian, Open folder as vault, pick it inside the mount. Notes are markdown files; a save syncs in under a second, and the laptop fetches note content as you open notes.
You can leave Obsidian open on both machines. Notes are separate files, and edits to different notes from different machines converge cleanly. Nothing requires closing the app to switch desks.
Two rules of thumb keep the vault tidy:
workspace.json, the window-layout file both instances write continuously. They contain layout, not notes. Delete them freely.If you prefer zero conflict noise, use the vault from one device at a time, like a notebook carried between desks. That is the tidy pattern, not a requirement.
The vault's .obsidian directory (settings, workspace layout, plugins) syncs with the vault. Same settings on both machines is usually what you want; the layout file is the one churn point, covered above.
Any notes tool that stores plain files (Logseq, Zettlr, plain markdown folders) follows the same recipe and the same one-device-at-a-time pattern. Tools that store notes in a single always-open database follow the database hand-off pattern instead.