Understanding Laravel Development of Applications vs. Sites

I have begun the beginning processes of learning Laravel. I am well versed in PHP but only recently decided to dive into frameworks vs. custom. What I am trying to wrap my head around is using the Laravel framework for small applications for an existing site vs. creating an entire site with Laravel. I am a back end developer, developing applications for various different projects. I need to understand how I can integrate independently developed Laravel applications into the same site.

So far I've followed the installation instructions and set up a Ubuntu VM with a LAMP stack + git + composer. I've installed Laravel and set the /public/ directory of the Laravel project as the site root. This process makes sense if I can creating an entire site using the Laravel framework.

However what if I have an existing, custom site, that with its own Home/About/Contact/ETC pages. But now I am looking to develop a small application for said site using Laravel .. lets say .. a application to manage an inventory of products. Normally if it were a custom application I would maybe create a unique directory for it in the root and have all my controllers + views stored there. I am having a hard time understanding how I would do this with Laravel.

Also, what if I were to develop two separate applications with Laravel -- Applications which were significantly different. How would I run both Laravel developed applications on one site? Would I have two instances of Laravel installed to ensure the correct configurations is setup? What would that look like?

I really appreciate any help that can be provided!