In this context, "threads" is a synonym for "logical cores", i.e. total amount of logical cores, regardless of how many physical cores implement them. Not extra threads.
Your CPU has 6 logical cores, so booting Linux on it "sees" 6 CPUs.
Your CPU has 6 physical cores, so each logical core has a whole physical core to itself, rather than having a pair of logical cores sharing a physical core with Intel's SMT, which they call Hyperthreading.
I've used other Intel and AMD processors, and usually when the product says 6 cores/6 threads the total amount is 12
. Terminology like 2c4t (2 physical cores, 4 logical cores) has been standard for many years, across all architectures, not just x86.
I've never seen anything described as N "real" cores + N "extra" threads because that's not how it even works. Both logical cores are "symmetric", it's not like one had to be started up specially. They each act as full CPUs. (When one is in an idle deep sleep, the other one can go into single-thread mode and get all the execution resources. When both are asleep, the physical core can actually sleep)
Fun fact: OS support for hyperthreading lets the OS tell which logical cores share a physical core by reading CPUID data, and/or APIC / LAPIC interrupt-controller stuff. An OS that wasn't aware of hyperthreading would still boot up and see however many logical cores the CPU supports (HT was enabled in the BIOS), and I think everything would just work except that it might schedule 2 tasks onto cores that compete with each other for execution resources, while leaving other physical cores idle.
Some CPUs have more than 2-way SMT. e.g. Xeon Phi has 4-way SMT (4 logical cores per physical core) as a way to hide memory and ALU latency and get good total throughput without a lot of out-of-order execution resources.
IBM POWER uses 8-way SMT on big physical cores.