I just took screenshots of an Android green text bubble and the https://www.android.com/get-the-message/ site, and used Photoshop's eyedropper tool to compare colors. They're the exact same shade of green, #48dd8f.
But it's not just you! The green on Google's site looks visually brighter because the entire bubble is on a blue background. On iPhone, the green is normally on a white background.
Now, try setting your iPhone to Dark Mode in Settings, and you'll find that the green bubbles are still #48dd8f green and the text is still #ffffff pure white; it's harder to read on a black background, IMO.
Could you upload a screenshot from your phone? Searching images online I see plenty that roughly match the colors they're using on the video/website, but none as dark as your iPhone. Reference: https://i.imgur.com/PlGjjQg.png
The background color of the bubbles changes in a gradient kind of way, depending on their vertical position on screen. That may explain the disparity you're seeing.
But it's not just you! The green on Google's site looks visually brighter because the entire bubble is on a blue background. On iPhone, the green is normally on a white background.
Now, try setting your iPhone to Dark Mode in Settings, and you'll find that the green bubbles are still #48dd8f green and the text is still #ffffff pure white; it's harder to read on a black background, IMO.