The primary goal in undertaking therapy/counselling is for you, the client, to feel better.
With coaching, there is a focus on some other tangible goal/s that you are pursuing. That might be enhancing your leadership skills, identifying your career direction, supporting you in acquiring new skills towards a promotion, building up your confidence in social settings, creating more enjoyable personal relationships, etc.
Creating positive future outcomes is the primary concern of coaching, so resonances from the past are only explored where they are relevant to unleashing your potential.
Coaches also tend to work with clients for a defined period of time, so you can expect to sign up to work with a coach for six sessions or three months, rather than open-ended, as is common for therapy/counselling.
Some coaches also use insights and training from the practical psychology/counselling domain, to enhance their ability to help you, the client, achieve and accomplish. I specialise in Psychosynthesis psychology.