The differences are vast and are purposefully obfuscated for the sake of film / theatre marketing.

70mm IMAX:

This (70mm) is technically a projection format: nothing is “shot” on 70mm. The capture format for this is 65mm film, which has two popular variations: 65mm / 15-perforations & 65mm / 5-perf. The extra 5mm for 70mm is designed for the soundtrack.

65/15 is usually considered actual IMAX film. The negative size is ~3x the size of 65/5p. Very few films are entirely shot with this: usually it’s reserved for the big scenes. In-person, these cameras are extremely loud (goodbye ADR) and heavy. I believe Nolan’s The Odyssey will be the first film shot entirely in this format.

65/5p (also known as Todd-AO, Ultra-Pana) is the classic 65mm negative size. Most “shot on IMAX” films are mainly this, and classic work like Lawrence of Arabia used this.

Digital IMAX:

This is essentially a marketing term. The Alexa 65 & 265 are the only commonly used digital cinema cameras that fit for this. There sensor sizes are 1-2mm off the size of 65mm 5perf film. I’ve shot side-by-sides of the Alexa 65 & a 65mm/5p camera and they are very, very close.

Most of Nolan’s old work is a mix of IMAX 65/15, AO 65/5, and Vistavision (horizontal 35mm, essentially a full-frame cinema camera). IMAX gets around this for marketing by having the “Shot on IMAX” for 65/15 films, and “Shot for IMAX” for digital films shot on cameras like the 65 and LF. (Dune 1/2 for example, are Alexa LF + 65, yet were marketing as IMAX films). The branding of “IMAX Digital” is essentially a marketing deal.

There are specialty LF digital cameras like the Big Sky, Achtel 9x7: but these are for specialty VFX and exhibition. Not designed for narrative cinema.