Hi there,

we are using the K2 component to integrate a simple blog. A Joomla menu item is directly linking to K2 using the K2 -> Categories menu item type to list all K2 items form all categories. This looks like shown in the first screenshot marked with "menu"

To enable the users to get a listing of all K2 items related to a certain tag, we are using the K2 tools module with tag cloud functionality. However, the way the K2 items are listed when clicking on a tag in the tag cloud looks totally different (marked with "tag cloud"). Also, there are no options to configure the presentation of the K2 items in the K2 tools module properties.

imgur.com/a/InxSW

Our site is based on a Joomlage template (joomlage.com, Journey #98). What it looks like to me is that the way the items are presented is based on the template's CSS when using the menu and based on a different style (from K2?!) when using the tag cloud module. What we want of course is that items are presented always in the same way. How can this be achieved? Thank you :)

So I guess the solution to achieve what I want is creating a new template inand modify the way how the items are displayed, right?

Yes.
However you need to use overrides instead of editing core files
getk2.org/documentation/tutorials/174-templating-with-k2-and-the-concepts-of-sub-templates