In an article about NIST Post-quantum Standardization project I read about the security criteria of the proposed schemes and there was this table (Level I lowest security, level V highest):
Level I: At least as hard to break as AES-128 (exhaustive key search)
Level II: At least as hard to break as SHA-256 (collision search)
Level III: At least as hard to break as AES-192 (exhaustive key search)
Level IV: At least as hard to break as SHA-384 (collision search)
Level V: At least as hard to break as AES-256 (exhaustive key search)
If I understand it correctly, then (in classical way, not using quantum computers and the Grover's algorithm) for exhaustive key seach on AES-128 we need to go through $2^{128}$ possibilities and in collision search of SHA-256 we need to go through $2^{128}$ possibilities to find a collision (thx to the Birthday paradox).
So my question is - how does the security Level I and Level II differ? And the same - why is security of AES-192 lower than security of SHA-384.