To answer your questions, psychoanalysis is a kind of therapy associated with Freud, NLP is an umbrella term coined by Dr. Bandler for a set of ideas he developed on how minds work and some useful techniques emerge from that understanding, hypnosis is a way to help people to focus their minds and access more of them.
Different coaches use different techniques and any one coach may use different techniques for different clients and client issues.
Psychoanalysis and counselling are generally about understanding yourself or past events in order to find relief from mental anguish, whereas coaching is more focused on the present and the future and is for people who are broadly mentally healthy, but who are fed up with what they have and want something different.
My kind of coaching is primarily CBT - Cognitive Behavioural Therapy - in other words, we use our intellects through a phone conversation, to explore client situations and emotions, and the insights arising give us strategies for making positive changes. Central to my coaching is the role of hidden beliefs in the shaping of human lives. I sometimes use NLP techniques and you can see articles in my website on things like re-framing and dichotomic (black and white) thinking, Swish moves, and so on. I also use a raft of techniques I have acquired, learned and refined in my years of coaching practice.
Now let's look at your CHANGE ONE THING item - not belonging to a cliquey group and being undervalued at work. I call it "the playground mentality". In the playground right and wrong are trumped by popular and unpopular, and it's a shame because those school years are some of the most formative of our lives. As adults we should not need to endure such nonsense and a healthy culture at work would eliminate it, but it often doesn't, and cowardly managers are at the root of that.
How you tackle it depends as much on who you are and how far you're prepared to go as anything else. Usually there's a ring-leader; someone who is louder and more scary. People give them space and respect in order to avoid being attacked. Other group members support this "leader" to gain points and a kind of security, and so the dictatorship is self-sustaining.
Here are some ideas you might consider:
- Confront them
- Analyse the ring leader intellectually, and see what insights you can find to help you
- Leave the company
- Transfer within the company
- Involve your boss or HR
- Build alternative alliances
- Befriend them - show them a better way to succeed
- Shine and take a pride in not being a part of the clique
- Ignore them