Screen transitions are in-between-frames screens or effects. What transpires between screens—if anything—is up to system and/or the art director. At first non-existent moments in time between screens, transitions gradually showed more of their flesh as video games became more trying on their respective systems. The just-about-not-there transitions were almost usurped by loading screens with the advent of CD-based gaming systems. As the graphic capabilities of these systems improved and their processors became faster, transitions took on a more movie-like appearance, sporting interactive features and fancy effects with artful flair.
Keep in mind that the discussions on transitions herein do no refer to video game cinematics or cutscenes.
In their presentation (if nothing else) video games follow from the century-old art of cinematography. While games have used transition devices for different reasons than those found in films, the devices themselves are the same. With respect to the medium, Zettl (2005) has outlined the following major transition devices:
* Camera changes within a screen that cinematographically are cuts are excluded here.
** Zettl (2005) also refers to the jump cut, but as I have yet to see this in practice in a video game, I decided not to include it in the list.
In the video game medium, loading screens can act as either a separate screen or a transition device. Arguably, loading screens are always separate screens, preceded and proceeded by cuts.

No More Heroes sports two major types of transitions: loading screens and special transition effects. Its loading screen is covered in this article. Of particular note is the latter transition, of which there are two examples in the game.

The first (comprising the majority of transitions) involves real-time rendered freeze frames of the current and next screens decked out with contrast and colour filters on the fly (see the image above). The second is a cinematic of "cards" being slapped down on the screen, each featuring a wildly coloured version of the same image: the respective boss the player is about to confront (featured to the left). This unique transition for boss battles is itself a point of "specialness" that both entices the player and punctuates the importance of the area of gameplay following it (plot-wise, these transitions indicate a crisis and eventually the climax).
References:
Zettl, H. (2005). Sight, sound and motion: Applied media aesthetics. Belmont, CA: Thomson Wadsworth.