That’s cause each Roku device is different. Care to elaborate on exactly what channel this is happening on and what show you are watching? Are they both the same Roku devices? Is this on Hulu? Netflix? HBO Max? The Roku Channel? YouTube TV? Disney+? More information would help. Are both Roku’s signed into the same account?
Roku OS 10 introduced a new feature labeled "Instant Resume". Basically, this allows you to continue watching a show/movie on certain channels by relaunching a supported Channel/app and selecting "resume" or "continue watching".
You can do this on either the same Roku device you were previously watching the content on, or another "linked" Roku device (another Roku device on same account/same email address).
The Instant Resume has to be programmed/coded into the Channel/app so not every Channel/app has this capability. This also does not work like you may be familar with previous cable/satellite DVR systems. (You don't just push pause and then just turn on your other TV and start resuming where you left off). It does act very similarly though, but involves a couple more button presses.
I have not seen a complete list of all Channels/apps that currently support Instant Resume, other than Roku's literature and some 3rd party literature mentioning "15+ channels...including AT&T TV, FilmRise, FOX Business Network, FOX News Channel, Fubo Sports Network, HappyKids TV, Plex.tv, STARZ and The Roku Channel. (I guess we can update this list if others add some confirmation of other channels).
It is a little misleading to term it "Instant Resume" as leads one to believe it automatically resumes. It really just provides user the "option" to resume. (at least currently).