Am I understanding how oAuth works correctly?

Question

OAuth

user accesses webclient_myproject_ru
CASE #1 - No token
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the application redirects it to auth_myproject_ru
where a form for authorization / registration appears
after the user logs in / registers, we
redirect him back to webclient_myproject_ru
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CASE #2 - There is a token
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make an ajax request to auth_myproject_ru ,
if SUCCESS comes in the response,
then EVERYTHING is OK, do a redirect to webclient_myproject_ru/home
if ERROR comes in the response,
then redirect to auth_myproject_ru
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