As mentioned earlier Presto creates "collections" of galleries and stores them within each instance of the template. If you want to create image galleries that have multiple collections of galleries you need to create a new instance of the Presto gallery and assign it to the menu item where you want the additional collection of galleries to appear.
In Joomla 3 it is possible to create additional instances of a template by using the save as copy or duplicate function in the template manager and the template administrator area.
Now that you have two instances of the Presto template with unique galleries created you can assign these instances to specific menu items. This article on our blog - How to assign a template to a specific page in Joomla highlights how to do this.
The menu items that you create to assign your galleries to need only be rferenced as links in the Joomla menu manager; ie menu separators or headings will not work for this purpose however links to article categories, single articles or featured articles will. The template overrides the display normally assigned to the menu item in question so the link used does not really matter.
Once you have followed the steps above you will have two different and discrete collections of galleries that are accessible for users from different menu items in the site.