Hi @Brijendra Gautam ,
Let me explain the conceptual difference between these two pages roughly. News post is a kind of modern page, and modern page also contains many other kinds of pages.
Per my understanding, first you should check whether you have published the news post, if the news post is just saved but not published, it is saved in Site Page library and will not appear in News Web Part until you published it. After publishing there may be a delay sometimes, just wait for a while.
However if you create a new page in the Site page library, it is likely to be a different kind of page instead of a news post, so of course it will not be displayed on News Web Parts. You can use the method in the link mentioned by sharatha to create a news post and make sure it is published.
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