What is the difference between personal consumption expenditure price and PCE quantity? What is the difference between these two things? How is PCE price different from PCE quantity? Also, I am confused about the difference between PCE quantity and measure of real output. For example, what is the difference between PCE quantity and Industrial Production?
Personal consumption expenditure (PCE) is the primary measure of consumer spending on goods and services in the U.S. economy.   It accounts for about two-thirds of domestic final spending, and thus it is the primary engine that drives future economic growth.  PCE shows how much of the income earned by households is being spent on current consumption as opposed to how much is being saved for future consumption.
https://www.bea.gov/resources/methodologies/nipa-handbook/pdf/chapter-05.pdf
The PCE price index is a measure of the prices that people living in the United States pay for goods and services. The PCE price index is known for capturing inflation (or deflation) across a wide range of consumer expenses and reflecting changes in consumer behavior.
https://www.bea.gov/data/personal-consumption-expenditures-price-index#:~:text=A%20measure%20of%20the%20prices,reflecting%20changes%20in%20consumer%20behavior.
Most PCE price indexes are derived by extrapolating consumer and producer price indexes from the U.S. Bureau of Labor Statistics.
The PCE quantity index derived by deflating current-dollar estimates at the most detailed category level by appropriate PCE price indexes with the reference year equal to 100.
Prices and quantities are prepared at a detailed level and are aggregated based on a Fisher chain-weighted formula  https://www.bea.gov/sites/default/files/methodologies/nipa-handbook-all-chapters.pdf#page=64
This source can provide some answers: https://www.bea.gov/help/faq/521
The difference between PCE quantity and industrial production is that PCE come from consumer spending.   Industrial production measures the output of the industrial sector, which typically comprises mining, manufacturing, utilities and, in some cases, construction.
The difference between PCE quantity index and real output is that PCE come from consumer spending while Real output comes from spending from consumers, business/industries, and government/government enterprises.