Does a user’s knowledge of operating system interactions carry over to a browser?

My coworkers and I recently discussed an article criticizing the hamburger icon + drawer navigation approach, and began to debate whether Window's "Start" button utilizes the same approach.

There are plenty of existing debates on the pros, cons, etc. of the hamburger, so I do not think there is a reason to continue that here. However, I would love to hear your opinion on how the "Start" button compares to the hamburger icon.

• Aside from user familiarity due to frequency of use, do you see a clear difference between the "Start" button and the hamburger icon?
• Are labeling, visual design, and/or icon position the only possible factors here?
• Do users' knowledge of operating system interactions carry over to a browser?

On a side note, does anyone know if the "Start" button heavily criticized when it was first released?

Edit: I should clarify that the hamburger menu I am thinking of for this example is fairly large (say 50+ items) and contains no alert/notification style content, just navigational links to pages within the website?