Lets dumb things down here:
A "Thread" is a software term, referring to the lowest level of execution. Essentially, a thread is a group of instructions that will be carried out in the same context. A program can have one to many threads. Odds are, your PC has several hundred, if not over a thousand, active as we speak.
A classical CPU core can execute one thread at a time. Some architectures however can execute multiple threads per core. The total throughput you get depends on the architecture and instruction load. Lesser forms of SMT (Simultaneous Multi-Threading) will only use a second thread on a core if the resources it needs aren't being used, adding very little to overall throughput. Some forms of SMT, however, duplicate almost all the CPU execution resources, so throughput essentially doubles. Some arches, such as IBMs POWER8, support more then two threads per core; in POWER8's case, EIGHT logical threads can be run per CPU core, thanks to SMT.
In any case, the Operating System, assuming SMT support, will always see the number of LOGICAL cores, which, if the CPU uses SMT, will be larger then the number of PHYSICAL cores. An Intel 2600k, for instance, is a quad core chip with Hyperthreading, which allows two threads to run per core. Windows and other OS's see the CPU as having EIGHT cores as a result. AMD's CMT operates much the same way. If you disabled HTT, the OS would see the 2600k as having FOUR cores.
To answer the second question: It depends. If the chips are two different architectures, then you can't know the answer, because maximum theoretical performance depends on several factors:
1: How many cycles CPU can perform per second (Clockspeed)
2: How many instructions per cycle the CPU can perform, on average (ICP)
3: How many physical cores the CPU has
4: How many logical cores the CPU has
5: The IPC gained when using the logical cores
6: The workload of the task who's performance you are measuring.
Typically, only the first and third are known for certain. Taking the classical case of Intel's Ivy Bridge versus AMD's Piledriver, you end up with many cases where a quad core chip running at 3GHz will beat an octo core chip running at 4GHz. Why? Because Intel's superior IPC ends up making up the performance difference, even though Piledriver offers more cores at a higher clock speed.
When comparing chips within the same CPU architecture however, you can typically assume more cores at a faster speed equates to a faster chip.