Are Seamaster 2252.50 and Speedmaster bracelets the same?

[DJE]

I have a 2252.50 Seamaster Professional 300m that I bought new in 2008. I also have a Speedmaster Pro moon watch that I bought on TZ around the same time. I haven't worn either one in years, but I pulled them down from the closet a couple of days ago. My wrist (like the rest of me, alas) is a bit bigger than it was in 2008. I'm not seeing an extra link in the Seamaster box, but I found one in a small plastic envelope in the Speedy box. The bracelets look identical - are they the same, i.e. could I add the extra Speedy link to the Seamaster bracelet? I also have a Railmaster from the same era that came to me on a leather band with an unused steel bracelet - that also looks the same, I wonder if I can have the shop mix and match so I could wear the Seamaster on the new bracelet?

Thanks for your thoughts.