Exactly. What is currently touted as an Unemployment number should be renamed: "% of those who are seeking full-time employment but not currently full-time employed". Perhaps "Unfulfilled Job Seekers" might be a better term than "Unemployed".

The other measure should be "% of working age Households where household income is not at or above average living wage adjusted by region". Then that is a measure of income and poverty and not a measure of "who has a full time job"