Nothing. There is no difference. The two different phrases are simply part of the
evolution of the employee time management industry. "Time and Attendance" is the former name for these types of systems and "Time and Labor Management" is the newer, more modern name.
In fact, Time and Attendance systems were first called "TimeKeeping Systems" - and some still are. Time and Labor Management is a newer name for the industry because the time and attendance industry is now all about managing both time and labor. The time being managed can be either worked time (attendance) or absent time (absenteeism) so calling the industry and these systems by the name of Time and Attendance leaves out part of what is being managed - absenteeism time.
To those in the industry this name difference is an important distinction from Time and Attendance as much of the focus now is on managing labor and managing a company's labor force. The phrase Time and Attendance is in fact slightly incorrect for the employee time management software industry also because these types of systems track absenteeism just as importantly as they track attendance. Absenteeism Tracking is very important in many companies and in many labor contracts. Much of negotiations in labor contract focus around the amounts of given and allowable absenteeism in each union group so the Labor Management System must track and report on the actual amounts as they are planned or as they occur. Failure do so can be both costly in dollars and costly legally too.
The interesting part of all of this is that as much as the vendors have tried to change the names of their industry and their products they are still commonly known as time and attendance systems and time and labor management has not really made any inroads in to the public outside of the industry. Its a shame but thats reality.