Discouraged workers are a subset of marginally attached workers - BLS definition for that is: Discouraged workers, a subset of the marginally attached, have given a job-market related reason for not currently looking for work. Persons employed part-time for economic reasons are those who want and are available for full-time work but have had to settle for a part-time schedule.
Discouraged workers should really be considered as part of the group of people that are considered unemployed, and similarly with marginally attached more generally. The current situation includes many people that have been furloughed, with an expectation that they will be rehired, and a number of them are counted as being employed, which isn't right. Recessions recover very slowly, and there are some well-known curves related to that. Some businesses will permanently close, and these folks that have been temporarily furloughed my not be rehired as a consequence, and others may not be rehired for a long period of time as the businesses come back. Those that have lost businesses may start new businesses, but not until the economy stabilizes.
Underemployed population: Persons employed part-time for economic reasons are those who want and are available for full-time work but have had to settle for a part-time schedule. This should be a subclass of employed population.
A new concept, underutilized population, as a subclass of the civilian non-institutional population, is the combination of unemployed, underutilized, and marginally attached population. This term, underutilized, has a corollary in Canada as well, but not the marginally attached or discouraged worker categories. We know that the Canadians have something similar, so the concepts belong at the EI level, but we'll need to reach out to StatCan to get the definitions from them (to update the US definitions if required).
From OECD - persons that are temporarily not at work (temporarily absent) - Persons temporarily not at work because of illness or injury, holiday or vacation, strike or lockout, educational
or training leave, maternity or parental leave, reduction in economic activity, temporary disorganisation or suspension of work due
to such reasons as bad weather, mechanical or electrical breakdown, or shortage of raw materials or fuels, or other temporary
absence with or without leave should be considered as in paid employment provided they had a formal job attachment
Currently, people furloughed due to COVID-19 are not consistently tracked, and many are tracked as employed but temporarily not at work, which will mean the data doesn't make sense if their employers do not recover. We need this subclass of employed population as well. But for COVID, we should create a new subclass of unemployed, which is unemployed due to temporary furlough or other economic reason (temporarily laid off) - see http://www.ilo.org/wcmsp5/groups/public/---dgreports/---stat/documents/normativeinstrument/wcms_087481.pdf.