Yes.  We charge a one-time fee for Passwords Plus on EACH platform/OS that you use it on.  See Pricing for more details.

When you use Passwords Plus for the first time, you will create a Sync Account.  This consists of an email address and a Sync ID.  If you want to use Passwords Plus on another device, you simply need to log in with the same email address and Sync ID.  The Master Password needed to open Passwords Plus is the same on all devices since you’re accessing the same account on each.

The one thing we tell you during installation is to put your Master Password somewhere safe because if you forget it, there is NO way to recover your data.  We do this on purpose to make your data that much more secure.