What is the difference between weak and strong resistance

Question

I have read some texts about strong collision resistance and weak collision resistance, but I was unable to understand the difference. The only thing I can understand that there

Answer 1

I wrote this answer due to the comment of Alexander; All the definition are copied from; Cryptographic Hash-Function Basics: Definitions, Implications, and Separations for Preimage Resistance, Second-Preimage Resistance, and Collision Resistance by P. Rogaway and T. Shrimpton.

• preimage-resistance — for essentially all pre-specified outputs, it is computationally infeasible to find any input which hashes to that output, i.e., to find any preimage x' such that h(x') = y when given any y for which a corresponding input is not known.
• 2nd-preimage resistance, weak-collision — it is computationally infeasible to find any second input which has the same output as any specified input, i.e., given x, to find a 2nd-preimage x' != x such that h(x) = h(x').
• collision resistance, strong-collision — it is computationally infeasible to find any two distinct inputs x, x' which hash to the same output, i.e., such that h(x) = h(x').

Fact 1: Collision resistance implies 2nd-preimage resistance of hash functions.

Fact 2: 2nd-preimage resistance implies preimage resistance.

---

As Alexander noted, by the pigeonhole principle, when the input space larger than the output space of the hash function the collisions are inevitable.