In volume test, large amount of data is handled in a short period. The no. of users may not be much and may even be one.
In Stress test, large No. of processing transctions are handled in peak period.The No. of simultaneous users using the software is more.
The secret of successful management – Evenness of mind
The test tool and scenario can be almost identical (except for few things).
The difference is the purpose.
It doesn't have to be specific. Idea behind volume is to figure out how much it can handle within specified environment. This includes, time, duration, number of users, memory or what-ever else is within your defined parameters. For example, good exmaple for requirement would be "Product will run with <=50% cpu usage, <=100meg of memory, and each instance <=10 second response time for 3 hours.". So, in your volume test, you need to creep up the test number and verfify that for given x load, it will not exceed these numbers. If parameters are not specified, you need to define artificial ones as goals.
Load test: Load test can have three fold purpose. 1.) Given the requirement, how long can it maximum defined load? The other one often is 2.) What is the maximum number it can handle before it misbehaves? 3.)If the product is pushed to it's limits, how will the software behave?
These may have slightly different twists, but you should get the idea.