Can family of EU Blue Card holder travel freely in the Schengen Area with a German Aufenthaltstitel? [duplicate]

I'm an American citizen working and living in Germany on an EU Blue Card. My family (wife and 2 children) is here with me. We were all issued standard German Aufenthaltstiteln (residence permit cards) by the Ausländerbehörde in our district. My card has an "Art des Titels" (permit type) of Blaue Karte EU (EU Blue Card). My wife's card and children's cards have an "Art des Titels" of Aufenthaltserlaubnis (residence permit).

I know that as an EU Blue Card holder I can travel freely in the Schengen Area. Can my family also travel freely in the Schengen Area, and if so, can they travel by themselves or do I have to be with them? I asked the Ausländerbehörde agent during our appointment and she answered yes to both questions. But now that we have the cards, I'm confused, because I thought the right to travel freely in the Schengen Area beyond the visa-free 90/180 rule was granted by the Blue Card program, while a "regular" residence permit in an EU country does not grant this right. (At least that was my understanding, any part of which may be totally wrong!)

My Aufenthaltstitel says:

Art des Titels

BLAUE KARTE EU

Anmerkungen

19A I.V.M 2 ABS.1 NR2A BESCHV PASS(-ERSATZ)-NR. XXXXXXXXX PASS GÜLTIG BIS XX-XX-XXXX SIEHE ZUSATZBLATT

My wife's Aufenthaltstitel says:

Art des Titels

AUFENTHALTSERLAUBNIS

Anmerkungen

32 ABS. 1 NR. 5 PASS(-ERSATZ)-NR. XXXXXXXXX PASS GÜLTIG BIS XX-XX-XXXX ERWERBSTÄTIGKEIT GESTATTET

My children's cards are the same as my wife's.