The key point of the comparison is than in React, as in immediate mode, you tell what you want shown every time (for every "frame") as opposed to having references to and controlling instantiated widget objects (an object graph).
In React's case, you tell it declaratively (your JSX component tree) with some procedural stuff thrown in (JS parts in the JSX). In classical immediate mode, by calling paint functions. But in both cases you tell every time - as opposed to performing actions on a pre-created widget graph. With the caveat that in React's case, behind the scenes, there is a widget graph, the DOM. But that's an implementation detail, as far as the dev writing React is concerned, they re-describe every GUI state.
So, you can say that React is an "immediate mode" abstraction over the retained DOM. In fact that's exactly what devs say about it:
https://twitter.com/ibdknox/status/413363120862535680
That's the inspiration from "immediate mode" that React brought - the GUI intention described by creating a new state, as opposed to manipulating state. And the diff algorithm is also inspired by the diffing algorithms used in immediate mode to draw less for each frame.
That React does this with DOM widgets under the hood as opposed to painting commands, and that those are higher level widgets and not lines and rectangles is not the part of the analogy people emphasize.
retained: user instantiated widgets, and changes their state (e.g. to clicked).
traditional immediate: for every 'tick', user issues commands to draw the new GUI state, usually with some smart diffing under the hood to minimize paint commands.
React immediate: for every tick, user describes the arrangement of widgets, text, etc for the next GUI state, usually with some smart diffing under the hood to minimize DOM changes.
Calling a "draw button" function, as opposed to declaring a "" in a JSX structure, is not that crucial of a difference, compared to the conceptual change between "manipulating objects" and "telling everything about how the UI should look at each tick".
Heck, a dev doing an "actual" immediate mode could trivially wrap the "draw button" function call to be driven from a declarative file (if you parse the term "button": call draw button, etc). It still wouldn't be retained mode.
And React and co also inspired interest in immediate mode GUIs, and inspired some new actual bona-fide immediate mode, with graphic calls and everything.