"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.
For example, if I exercise for half an hour on my treadmill every night, I could say I go walking, or perhaps that I walk, but I would probably not say that I go for a walk (unless joking).
If I travel to my office on foot, I would say I walk to work, but probably not that I go walking to work, or take a walk to work. The second sounds vaguely odd as if we were mixing activities (are you going walking or are you traveling to work?). The last, similarly, makes the trip out to be more important than the destination.
And if I would like to take my date through the park after dinner, I would suggest we take a walk or go for a walk. To go walk, without a destination in mind, would be a cheap but rather unromantic activity; to go walking is right out.
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.
Let's go for a spin in my new car.
∅ Let's go spinning in my new car.
A spin in the first example, as Oxford notes, is
A brief trip in a vehicle for pleasure
for which spin has no equivalent verb meaning. Even worse, consider
He went for a trip in Mexico [i.e. he chose to travel in Mexico].
He tripped in Mexico [i.e. he caught his foot on something while walking and stumbled]
He went tripping in Mexico [i.e. he went under the influence of hallucinogenic drugs]
If walking is something you do regularly as a form of exercise, then you can certainly say:
I need to go walking.
If you've had a hard day and need to take a leisurely stroll, then you would say:
I need to take a walk.
The construction to go ...-ing is commonly used in reference to planned leisure, athletic, exercise activities: skating, surfing, skydiving, hiking, biking, swimming, climbing, etc.