I don't quite understand your question as there are so many variables to consider. For example, what the design in question is for? If your talking more in general terms then Design for Print is on the decline for obvious reasons, hence why it is more difficult to find Print work. But it is still there, still relevant and needed. And also probably the most popular form of design for most graphic designers. Motion graphics is a whole different 'thing.' For one, you are comparing still design, to design with movement and often sound. While the same basic thinking and knowledge of design is applied, they are two different concepts. Motion graphics cannot have the same effect or be used for the same purpose as printed design and printed design cannot have the same effect or be used for the same purpose as motion graphics.
Again, it depends. Print trends are different to web trends. With regards to web I'd say at the moment it's 'flat design', which we see across apps and websites, as well as fullscreen, bold, clean, minimalist designs, though you could argue that this is simply modernism (the basis for contemporary design). Have a look at some creative agency websites and you'll see some trends straight away. A lot of them have a very similar appearance and functionality, almost to the point where they're not particularly original or exciting, which I guess it why design trends should be avoided in the first place.