Boltzmann distribution has the form $$ p_i={1\over{Z}} e^{-\beta E_i} $$ for the probability of a system to be in the state $E_i$. $E_i$ is the total energy of the system. For example if in $i$th state all the particles have the same energy $\epsilon$, than $E_i=N\epsilon$, where $N$ is the total number of particles in the system as I've understood from this notes.
On the other hand the same formula is used for the probaility of finding the single particle of the system in the state $\epsilon_i$
$$ p'_i={{N_i}\over{N}}={1\over{Z}} e^{-\beta \epsilon_i} . $$
Are both of these statements correct? Dont they contradict one another? I also find it confusing that in the Wikipedia article both system and particle states are labeled by the same symbol.