Here are highlights of the responsibilities of a webmaster to make the answer

The very first obvious answer to this question is because a webmaster holds more responsibilities than a software engineer. Here are highlights of the responsibilities of a webmaster to make the answer clear:

ensuring that the web servers, hardware and software are operating correctly
designing the website
generating and revising web pages
replying to user comments
examining traffic through the site.
So you can see the duties of a webmaster and how he/she have to manage across the designing as well as marketing of the site.
These points are suffice to conclude that a webmaster need to be smarter than a software engineer as he/she have to travel through a wider horizon of knowledge as well as practical implementation of that knowledge , that only a webmaster can have.

This broader definition of webmaster covers not only technical aspects of overseeing website construction and maintenance, but also managing website content, advertising, marketing, and order fulfillment.
Core responsibilities of the webmaster may include the regulation and management of access rights of different users of a website, the appearance and setting up website navigation. Content placement can be part of a webmaster's numerous duties, though content creation may not be.

Some webmasters of larger sites may also deal with heavy volumes of email, which are often questions related to the content on the website or general computer-related inquiries.

Whereas a software engineer is an engineer who applies the principles of engineering to the design, development, maintaining, testing, and evaluation of the software and systems that make computers or anything containing software work as per the wikipedia definition.

Please note the last line of the definition which says that a SE makes a computer or anything containing software work. So what about the parts not related to computer?? Anyone can probably wonder this. Here is the answer- a webmaster handles rest of the part.

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