While Contacts are simply a record of that person and their details...just like in your phone, a User is someone that does stuff within your Beeswax account. Users are the people in your business.
A User therefore starts out as a Contact and only becomes a User after they have been sent an invitation.
They may very well have a Beeswax User already. Such as in the situation they have an account of their own which they use to run their own business or they may have been invited in by someone else.
Either way they will only appear as a User under your Beeswax account once they have been sent and invitation and more importantly, have accepted your invitation.
So before you can invite someone into your Beeswax account you first need to create a Contact for them. Only once a they accept your invitation (and set their password) do they become a User with access to your Beeswax account.
By the way, you don’t have to send an invitation to anyone unless you really wish for them to become a User and gain access to your Beeswax account. And really you only need to provide access for someone in order for them to do things within your Beeswax account. ...like, create and manage projects or work on tasks that you wish to assigned to them. Or, in the case of your book keeper, reconcile your bank statements, etc. You get the idea.
So, a Client for instance, who you simply wish to send invoices to, does not need to be a Beeswax User in order to receive those invoices via the Beeswax system. They can simply exist as a contact forever.
By the way you can send invoices to any Contact that exists within your Beeswax account even if they are not a User.
A freelancer or external contractor may very well need to be invited into your account so that you can assign Tasks to them or give them access to Files within a project.
A Client, however, generally won’t need access, and more often than not shouldn’t need to access your Beeswax account. They don't need see all the Tasks or associated communication that relates to the Project. . .unless of course you have a very good reason for this..