NHS Choices is an excellent website providing reliable information on health matters, including mental health, for the general public both inside and outside of the UK. I discovered that their website (link here) has some very nice and simple descriptions of what counselling (counseling for our US colleagues) and psychotherapy are, also including a description of CBT. Below are some extracts of their descriptions:

Counselling:
Counselling is a type of talking therapy that allows a person to talk about their problems and feelings in a confidential and dependable environment. A counsellor is trained to listen with empathy (by putting themselves in your shoes). They can help you deal with any negative thoughts and feelings you have. Sometimes the term “counselling” is used to refer to talking therapies in general, but counselling is also a type of therapy in its own right.Counselling can help you:
  • cope with a bereavement or relationship breakdown
  • cope with redundancy or work-related stress
  • explore issues such as sexual identity
  • deal with issues preventing you achieving your ambitions
  • deal with feelings of depression or sadness, and have a more positive outlook on life
  • deal with feelings of anxiety, helping you worry less about things
  • understand yourself and your problems better
  • feel more confident
  • develop a better understanding of other people’s points of view

Psychotherapy:

Like counselling, the term “psychotherapy” is sometimes used to refer to talking therapies in general. However, psychotherapy is also a specific type of therapy. It may also be described as psychoanalytic or psychodynamic. Psychotherapy is a more in-depth form of therapy than counselling, and it can be used to address a wider range of issues. A psychotherapist can help you explore your thoughts, feelings and beliefs, which may involve discussing past events, such as those from your childhood. They’ll help you consider how your personality and life experiences influence your current thoughts, feelings, relationships, and behaviour. This understanding should enable you to deal with difficult situations more effectively. Depending on your problem, psychotherapy can be short or long term. Adults, young people and children can all benefit from psychotherapy. Sessions can take place on a one-to-one basis, in couples, families, or in groups whose members share similar problems.
Cognitive Behavioural Therapy:
Cognitive behavioural therapy (CBT) is a talking therapy that helps you understand the links between thoughts, feelings and behaviour. This allows you to manage your problems by helping you change the way you think and behave. CBT doesn’t remove your problems, but helps you manage them in a more effective way. It encourages you to examine how your actions and thoughts can affect how you feel. It’s based on the idea that the way you think about a situation affects how you feel and act. In turn, your actions influence the way you think and feel. It’s therefore necessary to change both thinking (cognition) and action (behaviour) at the same time. CBT is an active therapy, and you’ll be expected to work on your problems between sessions, trying out different ways of thinking and acting, as agreed with your therapist. The aim is for you to develop the skills to become your own therapist. CBT is usually a short-term treatment. For example, a course may consist of between 6 and 24 one-hour sessions. The National Institute for Health and Care Excellence (NICE) recommends the use of CBT for:
  • depression
  • anxiety
  • panic disorder
  • obsessive compulsive disorder (OCD)
  • post-traumatic stress disorder (PTSD)
  • long-term illnesses
  • eating disorders, such as anorexia and bulimia
  • schizophrenia

I suggest having a closer look at the website for more information.