Two products share the pane. The Formula tab reads the formulas already on your sheet; the LaTeX tab is an editor for writing an equation from scratch — or for taking one off the sheet and changing it before it goes back. They are named for the language the equation is written in, which is the real difference between them.
The three buttons at the top of the tab reach back to the sheet and bring the selected cell's formula into the editor, in the same three readings the Formula tab offers:
Get Formula: Ref Name Value
They are green to stand out from the editor's toolbar beneath them — the same green the copy buttons flash, because this is the other place something arrives from outside the editor.
What arrives is exactly what the Formula tab would have drawn, expansion included — it is the same call behind both. From there it is yours to edit.