@tima58962683,
I am assuming that in the end, you want one caption track that has all the captions you will use: the new updated and the old ones that do not need updating. And in your screenshots, C1 is the original track and C2 is the new track.
Select the ones you want to move. Alt + Drag to the other track. They will copy to the new track and overwrite any captions that they replace. You can also first delete the unwanted captions in the new track if that works better for you.
We are copying, not moving, because there is an odd issue being explored with moving captions.
You must move your playhead to mark the existing timecode before the move/copy so that it will snap to that location when you drag. If you don't, you can accidentally move the timing.
Copy/pasting will work, but I find it confusing for many users because it gets into the reassignment of Ctrl + V in the timeline panel to only paste to the same track.
Tip that I keep forgetting: If you are using the default PR keyboard shortcuts, Ctrl + Alt + Up/down moves between caption segments in the active track, even if the track is not targeted. Regular up/down moves between segments in targeted tracks, even if they are not active.
Does this work for you?
Stan