You can cat /proc/cpuinfo to see information about your current hardware.

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From http://www.rebourne.org/chiparch.htmk
  arch   Description
  ====   ==========================================================================
  i386   386 AMD 386 

  i486   486 AMD 486 equivalents, later labeled as "586" and marketed against
         Pentium, also similar WinChip, Cyrix, IBM, NexGen (bought by AMD),
         using socket 5 and 7 i586 Pentium (MMX) AMD K5, K6, K6-2 (3D) and
         Cyrix 6x86, perhaps some IBM, plugged into Intel Socket-7, and VX, TX,
         HX chipsets  

  K5     basically = P5. P5 is the intel core on Pentiums and Pentiums MMX.
         i586 PPro AMD K6-3 would be the closest performance equivalent 

  i586   First Generation Pentiums MMX, 66Mhz to 233Mhz
 
  i686   PentiumII/III/4
         AMD Athlon (K-7)        
         i686 Celeron AMD        
         Duron (K-7 "light")
         The whole i686 category is roughly equivelent to the K6 category 
         roughly PPro = K6 
                 PII = K6-2 
                 PIII = K6-3 
 
  K7     The K7 is a completely new core, and could be approximated to a i786.
         Expect that the PIV is also a new core and could be approximated to a i786,
         but the 2 are very different. So the comparisons sort of end at this point.  

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In the terminology of the hardware hackers, these are considered the same
architecture (32 bit Intel, "i386" if you're looking in the kernel source tree).
There are a few optimizations, but the way they think is similar. Contrast a Sparc,
a Strongarm (found in many handhelds), or even Intel's own ia64 ("Itanium" if you
prefer them by name).