I am using the High-Low Tech (MIT) directions to program the ATTINY with an Arduino Duemilanove. So i am not sure how to burn the boot-loader,
You don't. With that core you will have to change the fuses using AVRDUDE (a command-line program) or a similar program.
Is the core is the software used to upload?
No. AVRDUDE is used to upload.
A "core" is essentially a C++ library the implements the Arduino API. A "core" can include amenities that make life easier for the user (you) like bootloaders, libraries, and examples. The Tiny Core includes an amenity not available in the MIT Core that simplifies changing the fuses.