Yep, it's all the same as on PS3. Primary account shares all content with other accounts and you can have multiple primary accounts. Excerpt:
If a user activates a system with his or her account, other users on
the system can use applications and enjoy some PlayStation Plus
benefits from that account, even if that user is not logged in.
If multiple users have activated the system as their primary PS4
system, deactivate it for each user.
Acutally you can; my brother is doing it with a friend, but it's tricky. It's like buying plus, having your account on both devices and interchanging devices with someone else.
Take: Skynet (my brother's PS4), and Cerebro (his friend's); Charlie (my brother's account) and David (his friend's).
There's an option in the PS4 that says something like: "Activate Device" for "Game" and for "Video", to activate a main account on the device.
David has Plus privileges on his account but his 'Active Device' is Skynet, and vice- versa Charlie has Cerebro as his main device. And they both have their accounts on both devices (main and secondary).
So on Cerebro are both accounts, Charlie and David. Charlie is the main account of that device but it's on David's house; and on Skynet too are both accounts, David is the main account, and it's in Charlie's house.
Basically David+ is playing with his account on Charlie's device, in his own house (as if he were a guest in his own device), and Charlie is playing in his house, with his account on David+'s, device.
Cerebro (in David+'s house): Skynet (in Charlie's house):
> -Charlie (Main) -David+ (Main)
> -David+ (2nd) -Charlie (2nd)
This way David+ can play online on Cerebro and on Skynet, because his account has plus, and Charlie can only play online on skynet because the main account of the device has plus and enables all accounts of the device to enjoy the plus privilege of online play.
And yes: anyone of them can buy a game and download/play them on both devices.
Best Answer
Disclaimer: It has been years since I have needed to do any of the bellow or need a second account, as such information may be outdated due to changes to the system software/PSN Policy
This can be done
First off you'd want to Log Out of your account so you can see a screen similar to this
selecting "New User" and then "Create a User" you'll be asked to either sign into PSN or create a new account. if your girlfriend doesn't have an account she can make one here otherwise just have her log in.
For Digital Game Sharing, you'd want to make your account as the primary account for that console. I do believe you can do this by signing into your account and then going to your user profile settings and looking for something like "Activate this console"
with this, you're girlfriend can now play any digital game you have brought and downloaded while having her own save games and trophy progression/collection. however it will not work in reverse as explained here on IGN
Since you're Girlfriend's account would be like if you was logging into a second console, she can log in and buy/download games with her own wallet but you will be unable to play them unless she is logged in.
Also remember that this does not affect physical games, ie. if she buys a physical copy of a game and plays it first, you can later play that game without her needing to be logged in. and obviously in reverse you don't need to set the PS4 as your primary console for her to play physical games you have brought and played first