You mean PC3-12800 and PC3-6400. That number indirectly refers to the peak data rate of the memory (see Wikipedia for technical details), which is influenced by clock speed and other communication details.
You'll have to check the specifications for your computer to see if it will actually make it faster. Some machines support multiple clock rates but not always.
It should work though; but may not make a speed difference. If your motherboard does not support the faster clock rate it will usually clock it down to the rate it does support, which may just be the PC3-6400 rate.
There's no worry about voltage issues. All PC3-* memory has the same voltage requirements (1.5V nominal, 1.975V absolute max). The only other DDR3 standards are lower voltage (PC3L-* is 1.35V, PC3U*- is 1.25V, nominal), so if your laptop uses those instead (which according to you it doesn't) worst case is it doesn't provide enough power. And even if you accidentally went the other way they all have absolute maximums greater than 1.5V.
You could just try it. You won't damage either the machine or the memory; if it doesn't work it simply won't recognize the memory (or worst case won't boot, in which case you take it out again and all is well).
Also, in case you are wondering: Unless something happened in the last 5 or so years to change this, generally all modules in a given machine must be the same type and size (don't quote me on size), and of course must match the list of supported memory given in the PC's technical specifications. Damage won't occur from using the wrong type though; just failure to function properly.
Don't be surprised if your old laptop doesn't support the faster memory, though. Set your expectations low.