Short answer: Registration may take place on another page and that will be fine, if this is well-thought and supporting organizational objectives.
What is a landing page?
A landing page is the page within a website which is meant to receive
your visitor directly and entices him to do something further. Thus it
acts like a door which receives a visitor, informs, attracts and
persuades him to perform an the activity and at the same time helps
the business achieve its goal(s).
There are several other definitions of "Landing Pages" and some of them make it mandatory for a landing page to have a form. I find those definitions are too narrow and incapable to explain lateral use-cases. For example, if I only tend to educate my user about a special offer through my landing page, I would have educated him/her and achieve my objectives if the user hand landed on the page and spent next 5 seconds on it. Need of keeping of form was not there and shouldn't be there. If such a page is not called landing page, what would you call it?
Coming to your question:
As per the conversion rules, only ask as much infiltration which is minimally essential. Getting forms filled is our business objective and by filling forms, user doesn't achieve his/her goals. If capturing email does the job for you, keep the burden low at user and let him provide only that bit of information which is essential for you.
If you are asking user for the email only and are looking to send information about product/service later, do consider these aspects,
- What is the risk user not reading the email and not returning to your site?
- If a user finds his/her email 5 hours later, would email have created the required engagement which would make user use that coupon?
- breaking user-flow into two stages VS in one go - is inherently less efficient. How much would you be loosing user's satisfaction by doing that?
- what alternates do you have to show user his/her discount coupon? Can you display that in browser without asking for his/her email?
- Is capturing email alone sufficient to propagate organizational objectives using other channels like email marketing?
I hope this will help you in making a decision.