Whats the difference/Restrictions/Rules for Android Alpha and Beta testing?

I wish to carry out pre release testing of my current Android Application.

My requirements for this testing are:-

My Application must not appear in the Google Play Store or...
Only invited testers can see the Applications Play Store Page

Only invited users can participate in testing.

Testers do not have to have a gmail account.

Total number of testers < 10,000.

Testers are automatically contacted with download link.

From what I have read (Chatted) on Google sites my choice is between Alpha or Beta testing.

for Beta testing

Open beta
Use an open beta when you want any user who has the link to be able to join your beta with just one click.
One of the advantages of an open beta is that it allows you to scale to a large number of testers.
However, you can also limit the maximum number of users who can join.

Closed beta
Using email addresses – If you want to restrict which users can access your beta, you have a new option:
you can now set up a closed beta using lists of individual email addresses which you can add individually
or upload as a .csv file. These users will be able to join your beta via a one-click opt-in link.

Closed beta
with Google+ community or Google Group – This is the option that you’ve been using today, and you can continue
to use betas with Google+ communities or Google Groups. You will also be able to move to an open beta
while maintaining your existing testers.

Beta satisfies almost all of my requirements however I cannot allow my application to be searchable on the Play Store and I do not want to require my testers to have/use a gmail account so Beta testing is out.

So my only choice is Alpha.

I am still not clear on the "flavours" of Alpha testing available.

If I have to manually distribute the Alpha app link why do I upload a list of emails?

What purpose does the uploaded list of emails have?

Is the list of uploaded emails used to control access to the Alpha apk?

Can I run Alpha test groups of 1000's of testers.