That kind of bootstrapping is different, and more of a colloquialism.
'Bootstrapping' more or less means 'getting initial software loaded' in both cases, but the kind mentioned here is for a computer that only has basic DOS operating system files installed, and you dont have another means of getting files in or out of that machine. (Say, files are too big for floppies, dont have floppy disks, or lack floppy disc drives. Dont have cdrom drives, or have a means to attach that computer's hard drive to another computer to put more software onto it.)
You can use MODE to configure a serial port, then CTTY to make a very primitive null-modem connection, then send a more robust serial data transfer program over, then use that.
Pushing that more capable program over this way is 'bootstrapping' the connection.
Most of the time you see that word though, it's in the context of the computer being turned on, and starting an operating system.
Modern computers have a pretty complicated bit of software baked into their motherboards, call the Extensible Firmware Interface, or EFI, but old computers have something much more limited and comparatively primitive, called Basic Input/Output Services, or BIOS.
When an old computer first powers on, it's CPU begins looking for a program to run, starting at the very bottom of memory (segment 0, offset 0, address 00000000). This program is part of the BIOS, and walks the processor through various Power-On Self Test (POST) routines, which make sure the system RAM is good, that external storage devices work and respond when accessed, and that there are no bus conflicts, among other things.
After it does all that, it's ready to start an operating system. It pulls the first 512 bytes from disk devices it knows about, and tests to see if that data contains a small program to execute or not. If not, it moves to the next one in the list until it finds one that does. If it fails to find one at all, it notifies the operator then waits for user input.
This process is *also* called bootstrapping.
The small 512 byte program that the bios post routine loads into memory is called a 'boot loader', and the special sector it loads from is called the 'boot sector'.
This program can be anything, as long as fits in the sector. DOS, WinNT, OS/2, Linux-- all start the same way up to this point, and each of them use different ways of doing things *after* this point.
Regardless, the job of this tiny program, is to copy more data into memory, like disk drivers or OS services handlers, then set up shop. It 'bootstraps' the computer into a functional state.
When most people say 'bootstrap' they mean this latter, but the former is also a correct useage.
Just dont confuse the two.