In the second image, one way to achieve this is to
- select a narrow area that spans (width) the entire image and is only confined to the grass area.
- copy that to a new layer (Cmd+J/Mac Ctrl+J/PC in Photoshop).
- change to that layer and do a free transform (Cmd+T/Mac Ctrl+T/PC).
- stretch the selection vertically until you have what you like.
- then change the layer blend mode to something like multiply. You'll have to play around with the blend modes.
This is a reliable way to get a vertical blur effect like the one you've shown. Another way, as @RedGrittyBrick mentioned is to do the same copy of the grassy area, then use a motion blur with an angle of 90 degrees. Again, blend modes will make this look more natural.
Duplicate the layer and use filter>distort>wave then use motion blur to soften the effect and lower the opacity to further soften. Use a layer mask to remove the effect from foreground objects.
I'd guess vertical panning to blur background in ambient light with flash to freeze foreground trees. Perhaps continuous light on grass and off-camera flash to illuminate first rank of trees beyond grass.
I would say these two images use different approaches. The first appears to me to be a dual-shot effect done in-camera, or two shots taken in camera and merged in post. The second appears to be an entirely digital effect.
The "In search of adventure!" Shot
The tree shot appears to be two shots done in-camera and either blended with a DSLR camera feature that supports it, or blended in post. The first shot would have been a longer exposure, with some vertical camera movement. A skilled hand could achieve the vertical blurring if it was steady, however you could also probably get fairly clever with a macro focusing rail. The second shot would have been a stable tripod shot. I am going to assume that the first and second shots were of slightly different things, rather than being taken at the exact same spot. The blending of the background appears to fade into the foreground of the second shot in a somewhat abrupt way, indicating that the tall thin trees of the background came from a different location. The second shot would have needed a fairly clean background, or a background that was either bright or dark enough to blend properly with the second shot (assuming in-camera blending). If the shots were blended in post (seems more likely), then the foreground in the lower part of the shot and the foreground tree itself would have been masked and blended into the background.
The "Spring" Shot
While I have seen shots like this that are indeed the result of multiple directly-blended exposures, usually involving longer shutter times and vertical camera movement, this shot appears distinctly digital in its processing. It also appears as though it too may have been multiple shots...one for the background which had one form of processing and one for the foreground which had a different form of processing. The background shot seems to be slightly out of focus and lit differently than the foreground shot. The vertical streaking could be a new entirely artificial layer blended on top of the background layer, or it may have been some careful processing of a copy of the background layer itself. A simple motion blur filter would probably do the trick. The foreground layer appears to have been processed similarly to the background layer, however more selectively. The streaking on the upper and lower edges of the foreground layer seems to be based solely on the top and bottom rows of pixels. That would require duplicating the foreground layer, cutting out the middle rows of pixels, and vertically motion blurring what remained. All of the layers are blended, probably with multiply or basic opacity.