Vulnerability assessment is the process of identifying and quantifying vulnerabilities in a system. The system being studied could be a physical facility like a nuclear power plant, a computer system, or a larger system (for example the communications infrastructure or water infrastructure of a region).
A penetration test is a method of evaluating the security of a computer system or network by simulating an attack by a malicious hacker. The process involves an active analysis of the system for any weaknesses, technical flaws or vulnerabilities. This analysis is carried out from the position of a potential attacker, and can involve active exploitation of security vulnerabilities. Any security issues that are found will be presented to the system owner together with an assessment of their impact and often with a proposal for mitigation or a technical solution.