The specifics may vary by company. Considering that you've applied and interviewed, you should already be familiar with the job postings provided by the companies and have points of contact (such as Human Resources, the hiring manager, or your potential future supervisor) if you have additional questions.
Generally speaking, though, someone with the title "Configuration Specialist" tends to work in the field of configuration management. It deals with managing the version control systems, managing baselines and releases, auditing, build management (build scripts, nightly builds, automated build servers), traceability (requirements, design and implementation artifacts, bug reports, change requests, etc.), and so on.
Someone with the title of "Software Engineer" is more likely to deal with requirements, design, development, and testing of software.
At the end of the day, though, the title may just be an organizational designation. Different companies and types of companies may have different titles for the same types of roles or very generic titles that don't necessarily correspond to what your day-to-day function is. The only one who can provide a complete answer is someone from the company.