Formal definition that I have seen of concept class is
class of all true functions
and that of hypothesis is:
But most of the times they are used together. For example in definition of PAC
A concept class 𝐶 is PAC learnable by a learner 𝐿 using hypothesis space 𝐻 if for all concepts 𝑐∈𝐶, distributions over 𝑋, true error probability 0≤𝜖≤1/2, failure probability 0≤𝛿≤1/2, learner 𝐿 outputs a hypothesis ℎ∈𝐻 such that
True error less than or equal to 𝜖
Computational time is polynomial in 1/𝜖,1/𝛿, representation size of data object, and representation size of concept
What is the difference?