Q:

Invoking interpreter as python3 vs python3.2

Is there a difference? 
I am assuming no since neither Chapter 2 of the tutorial nor any of my searching on S.O. and Google have revealed anything.  
I did an md5 sum of my python3 binary and the python3.2 binary and they are the same. 
For curiosities sake I just wanted to know if it is like running sh on a system with only bash in compatibility mode or something like that. 
EDIT: to be clearer this is Mac OS X with Python 3 installed from python.org using the Mac OS X installer.  They are not symlinks but actually two separate binaries.  From the answers provided and they way they are symlinked on other systems tells me, No there is no compatibility mode or anything like that and just use python3. ;)  Thanks. 

A:

You don't specify your operating system, but on Ubuntu (and probably lots of other systems) it's normal practice to link python and pythonX to pythonX.Y.  On my system, I have 2.7 installed, so python and python2 link to python2.7.   Likely you have something similar. 
I'd generally recommend using the least specific name which guarantees what you need.   If all you need is python of any particular version, then call python.   If you need version 3.X, then call python3.   If, for some reason, you need python3.2, then call that.   Being as unspecific as possible means less updating as new versions come out and improves the chances that your scripts are portable to other systems which might not have your specific version installed.