Standard definition of conventional encryption

The standard definition of conventional encryption works as follows:

• There is no input data for the adversary.
• We choose a plaintext attack of one of two kinds:
  1. When asked to encrypt message $m$, the oracle returns encryption of $m$ under a fixed key that is chosen randomly initially.
  2. Oracle returns encryption of a randomly chosen message, totally independent of $m$.

The idea is that in the second case, the adversary gets completely useless data, and if they cannot tell this apart from the correct encryptions, then they cannot do any damage in the real world either.