More specifically, the device Obama was given was a Sectéra Edge [0][1] by General Dynamics, a device specifically designed to be able to operate on Top Secret voice and Secret data networks. It had hardware-level separation between the unclassified and classified sides, even having separate flash memory for both. [2]
The NSA contributed to the design and certified it and another device (L3's Guardian) on the SCIP, HAIPE, Suite A/B, Type 1, and non-Type 1 security protocols.
It was absolutely not a regular BlackBerry, it didn't run any RIM software, no data ever went through RIM's servers, and secure calls were encrypted and didn't use SS7. It was a clunky purpose-designed device for the entire US government to be able to access Secret information and conduct Top Secret voice calls on the go.
Even then, there were limitations to when and where it could be used and when a SCIF was required.
The current equivalent of the SME-PED programme is the DoD's Mobility Classified Capability[3], which are specially customised smartphones again made by General Dynamics.
There is no excuse whatsoever for the current administration's use of Signal, let alone TeleMessage Signal, for Secret and Top Secret discussions on regular consumer and personal devices. It's deeply irresponsible and worse than any previous administration has done.
[0] https://www.cnet.com/tech/tech-industry/obamas-new-blackberr...
[1] https://gdmissionsystems.com/discontinued-products/sectera-e...
[2] https://apps.dtic.mil/sti/tr/pdf/ADA547816.pdf
[3] https://www.disa.mil/~/media/files/disa/fact-sheets/dmcc-s.p...