By this time you should have a good understanding as to what is meant by the term Free Software by reading the About page and the Difference between Free Software and Open Source Software. Basically Free Software extends beyond monetary cost into the liberty of being able to view, modify, and redistribute code.
Freeware on the other hand is a completely different beast. Although both freeware and Free Software typically do not have any cost associated with acquiring the product, that would pretty much be where the similarities end. Freeware doesn't adhere to any of the F/OSS licenses. And the biggest difference probably being that you as a user don't have access to view or modify the source code of the product. In some cases, you don't even have the right to redistribute.
From a security perspective this should be very concerning. You have an individual offering to give you a program they spent time developing with sometimes no help from any other developers, and they are giving it to you for free. You are not allow to see what the program is actually doing on your system.
You as a user are making a couple of huge assumptions when doing this.
Assumption 1: That the developer(s) are honest and trust worthy and will not do any harm to your system either intentionally or unintentionally. Personally I think the majority of freeware developers are honest, well intending people who are only looking to help out other. But you most certainly have a set of less than scrupulous people or developers who are just not that good and writing optimized code.
Assumption 2: That the developer does not have any stolen code or copyrighted material in their application that doesn't already belong to them. This could prove very costly to your organization.