Subdomain is a secondary domain within your
website. your subdomain will look like subdomain.mysite.com. By using a subdomain
on your site you can create a lot of additional websites within your main site.
Multi-Site is a feature offered by some content management systems where you can create a lot of websites within your main websites. In order to
add multi-site functionality on your website, you will have to choose that option while installing content management system-CMS (I am talking about WordPress. I do not know about multi-site options on other content management systems).
When you create multisite, your website will look
like mysite.com/mutisite1, mysite.com/multisite2 etc.
Have you tried to create additional sites within
your main site?