One project specifically was born after a hard-fork (Ethereum Classic) and the other one still having value but, what differences can we find between these two project concerning the blockchain?
Technically the two are almost identical. Ethereum Classic is Ethereum but without the one-off state change that reallocated funds held by the DAO attacker's contract to contracts where they could be returned to their original owners.
The main difference is in the social layer: Ethereum Classic implicitly has a social contract based on the principle that code is law and the rules should not be changed.
In future it seems likely that they will diverge technically; For example, if and when Ethereum moves to proof-of-stake, Ethereum Classic may decline to adopt this change and stick with proof-of-work. Relatedly, Ethereum Classic has already made a change to remove the "difficulty bomb" which Ethereum developers originally introduced to force the network to accept an upgrade, which was intended to facilitate the transition to proof-of-stake.