"I need to go walking" Why not, "I need to take a walk."?
Are they the same or not?
Are they used in the same situations or not?
Each can mean something slightly different dependent on context, because each can carry certain connotations not indicated by the others. The degree to which the distinction is drawn depends very much on the audience and circumstances, however.
To take a walk (or to go for a walk) is to undertake a journey on foot, taking in the experience of the outdoor environment, the scenery, the interaction with other pedestrians, and so on. To go walking is to engage in a particular kind of exercise, which may imply the donning of walking shoes or other walking gear. To go walk is to move on foot at a comfortable gait.
The same holds for a number of activities where the word for one session or example of the activity is the same as the bare infinitive— to go drinking as opposed to go for a drink as opposed to go drink, and to drive, run, look, swim, drink, ride, fly, and so on. Note too that many words which are used both as nouns and verbs have multiple meanings, and the most common noun meaning may have little or nothing to do with the most common verb meaning.
A spin in the first example, as Oxford notes, is
for which spin has no equivalent verb meaning. Even worse, consider
If walking is something you do regularly as a form of exercise, then you can certainly say:
If you've had a hard day and need to take a leisurely stroll, then you would say:
The construction to go ...-ing is commonly used in reference to planned leisure, athletic, exercise activities: skating, surfing, skydiving, hiking, biking, swimming, climbing, etc.