Same hex code, appears differently on website vs video

Hello all,  

I have been working on my website and some sections of my website have a light gray background (#E3E3E3 to be precise). Because most of my work is motion based, I have some video clips that are presented as if they are on a phone or mac monitor. So because I want it to blend seamlessly with the light grey of my website, I made the background colour of my video file, the same colour (same hex code #E3E3E3) thinking it would blend in seamlessly.

However I have realized that even though i double-checked and see that the hex codes are all exactly the same there is a difference in them. On my PC display it's most noticable. On my macbook it seems to blend in better. I have on both my PC and macbook, done a "dropper" test and when I go on the slightly lighter one it reads as the intended hex code and when I select the slightly darker one it still reads the same hex code. 

It's one of those little details that I really wish to fix because I think it takes me out of what I intended to do. I have alternatively tried to export my videos in premiere just with a transparent background, so no grey at all, so that way it would blend with the background with no issue, however I cannot seem to rely on this method because the file sizes end up being extremely large even though they are short clips with no sound for the most part. 

Is there a solution to this? Any suggestions welcome! 

Thank you very much