Update: Safari introduced a feature accessible via the developer tools, which lets users capture screenshot of the entire webpage. This feature was not available at the time the answer was written. The original answer is kept as is for reference.
For Safari, refer to the answer by shawncampbell.
But, are there any keyboard shortcuts that can scroll a webpage or any other pages and get the screen capture?
No, there's no built-in mechanism in Safari/macOS to scroll and screenshot an entire webpage.
You'll either need to manually scroll, snap and stitch the images or write a script, both of which could be cumbersome.
You can do a Web search and find 3rd party Safari extensions that can perform this function for you, but again that's not what you are looking for.
If you relax the scope and are willing to download a software from the Internet, you can install Mozilla Firefox, a popular alternative Web browser for macOS. A screenshot tool, aptly named Firefox Screenshots is natively built into the web browser.
Download and install Firefox, open the desired Web page, click on the Page actions button in the address bar and select Take a Screenshot option.
You can choose between capturing the entire page,just the visible area or a specific region within the visible area.
What's great is that you can choose between downloading the generated image right away or save them online for later access (Do note that as per the linked support article, screenshots are saved for 14 days only). You can also copy the image directly to the clipboard or edit it in the browser itself.
Here's the Ask Different Web page in it's full glory :)
In my opinion, this is the most hassle free approach one can take to screenshot a Web page in macOS.