What is the difference between Planners and Schedulers , and what is the best for medium size projects to have planners or schedulers or both ?

Scheduling is a subsdiary of Planning.

In scheduling you just we do activity listing out, sequencing, dependencies and resource loading.

In planning, in addition to the above, covers creation and updation entire project management plan like {Scope, time, cost, risk, procurement, quality, communication, stakeholder management plans}.