The distinction is literally just in the scope. Large open market operation (OMO) is how QE is defined. See Fed definition of QE:
a large-scale
asset purchases—in the hundreds of billions of dollars range
There isn't really much more to it. OMO that is measured in hundreds of billions is QE.
The textbook is correct that QE had different goal than regular OMO, but goal is inconsequential for definition of QE.
The distinction is only about size. OMO is small asset purchase, QE is large asset purchase. However, historically some QE did focused on unconventional assets.
In the US there were 4 rounds of QE (see Fed here, here, here or here) :
QE 1 (circa 2009/early 2010): During this QE Fed purchased a lot of unconventional assets (which is what probably creates confusion in minds of many people about what QE is).
QE 2 (circa 2010/2011): This was in essence just large OMO, Fed mainly focused on buying large amount of treasuries.
QE 3 (circa 2012): Fed went back to purchasing unconventional assets.
QE 4 (circa 2020): Here Fed again changed course and purchased predominantly government securities (although some unconventional assets were part of QE 4 as well).
As you can see from the historic examples above, it does not matter what assets Fed buys. Convention or unconventional or mix of conventional and unconventional - all large asset purchases are known as QE.
Goals also do not matter, the QE 4, which was done to deal with pandemic, had clearly completely different goals from QE 1-3.
This is also just evidence from Fed around the globe different central banks also implemented QE with varying goals and varying assets included in the plans.
Suma sumarum what distinguishes QE and OMO is size. Up to some threshold X asset purchase would be considered OMO and above threshold X it becomes QE. For example, Fed considers asset purchases that can be measured in hundreds of billions dollars QE. Different countries and researchers might have different threshold X (since currency value varies and there might be some disagreements of what is large enough), but again generally its defined in terms of size.