From the license agreement:
Am I allowed to use FileMaker software that I've licensed on my computer at work on my home or portable computer?
In order to provide our customers with the flexibility to take their work home with them, we provide limited home/portable use rights for FileMaker Pro software. As long as you are the primary user of the computer at work, you may make a second copy of FileMaker software for your exclusive use on either a home or portable computer. Note that you may only make one such additional copy for either your home or portable computer, but not both. And only you, and no one else, may use the copy of the FileMaker software installed on such second computer. Please note that these rights do not apply to students if the software is part of a volume license program ordered at an education discount. Further, these rights do not apply to FileMaker Server software.
So can I be connected to my central FM database the same time on my PC and my laptop at the same time?
Nope. FileMaker will throw an error and then quit on the second link from the same license Key. The license permits you to use one or the other, but not at the same time when connecting to a hosted database.