I am interested in creating a site that is able to separate Men's and Women's collections into two different landing page sites (with two different types of images, etc.) Take Bershka for an example (https://www.bershka.com/us/women-c1010193132.html). If you click the top left bar it gives visitors a choice between Women and Men. When you click either option, it completely changes the pictures and products shown on the site.
Is this possible to do on Shopify?
Yes you can.
There a few options you can achieve this but the most straightforward will be to use a separate template.
You can create a template called collection.men.liquid and a template collection.women.liquid. You can add different images for both templates and from the admin panel you can easily set which products go in which collections. You can choose which template you will use for each collection from the admin.