Hello folks - I have an annoying problem.
No, its not my personality, that’s different! 
The problem is:
I access my gmail email on two devices - my android phone and my netbook. However, recently I’ve found that some emails to me show up on my android phone but are not showing up on my netbook. To the best of my recollection, I have not set up any preferences or anything. What could be happening?
Let’s narrow down the search a little:
Does the netbook use Windows? On your netbook, do you use the GMail Web site (www.gmail.com) to read your mail, or do you use a program such as Outlook?
On your Android phone, do you use the official GMail app or some other app, such as K-9 Mail?
Gmail introduced “Tabs” (Primary, Social, Promotions, Updates, etc…) , which is the version you most likely see with your notebook in your browser.
Your android phone does not make this distinction.
Your emails will show up on both devices, you just have to look in different places. On your phone, they end up in your standard inbox, on your Netbook, they might be in some folder/tab.
Could they have different spam filters and some of the emails either deleted outright or put into a Junk Email folder?
That’s the most likely solution. My Gmail inbox routes certain types of email to tabs, but the Android device does not differentiate in the notifications (though if you go into the Gmail app, the latest version of the software will show the tabs have new messages in them).
You can get rid of the tabs if you want to. If you go to Settings -> Inbox, unclick all of the “Categories” except for “Primary” (which is the default).
Thank you all, yes it was the Tabs. I clicked on “All mail” and the emails were there. And now I’ve gotten rid of the tabs as per your directions. Great - thank you!