Your link explains it pretty well. Note that it does not support your false claim that only people collecting UI benefits are classified as unemployed.
Unemployed is defined as did not work 1 or more hours for pay (or 15 or more hours unpaid in family business or farm) and weren't on sick leave, vacation or other temp abscence, and actively looked for work in the prior 4 weeks (those on temporary layoff need not have looked for work).
The Labor Force is Unemployed + Employed (all those working or trying to work). Everyone else in the adult civilian non-institutional population is "Not in the Labor Force."
The UE rate is Unemployment/Labor Force.
It is useful to look at those who are marginally attached....those who say they are willing and available to work but who aren't trying to get a job. This is limited to those who have looked in the last year, so it's known that they have actually tried to find work just not at the current moment. These are people who are likely to start looking for work...they're not available labor, they're potentially available labor.
The U-6 adds in "Part time for Economic Reasons:" those who, during the reference week, worked 34 hours or less, want and are available to work 35+ hours/week, but did not because either their hours were cut or they can't find a full time job. This let's us see the extent of those who were forced to work less hours than they want and are being underutilized. They're NOT unemployed, they're underutilized. So the U-6 is (Unemployed + Marginally Attached + Part time for economic reasons)/(Labor Force + Marginally Attached)
These two measures tell us different things. Th official U-3 tells us how much available labor is not being used at all. And the U-6 tells us how much available and potentially available labor and how much current workers are underused.
The U6 chart shows the true unemployment numbers. which is not the same number as 9.1
Again, how does it make sense to you that including people who are working and people who aren't trying to work is more "true" a measure of unemployment than people who are trying to work?
Add on that the margin of error for the Unemployment level is about +-2.4% while the margin of error for Marginally Attached is about +-5.7% and for Discouraged it's +-9.4%
And I'll remind you that just repeating things is neither an argument nor support for your claim. Oh, the the October UE rate was 9.0%
Part time workers do not equate to full time work. not according to the U6 the unemployment was at 16% or higher.