In April 2019 our economy created 263000 new jobs, however, total employment went down from March to April by103000 jobs. Why this difference? https://tradingeconomics.com/united-states/employed-persons

This link shows that total employment declined from March to April even though we added 263000 new jobs. Can someone explain why?
The main difference comes from the source of the data. While both figures can be found in the latest BLS report, the +263K comes from their establishment survey, which includes only non-farm jobs as reported by employers.


  Total nonfarm payroll employment increased by 263,000 in April, compared with an average monthly
  gain of 213,000 over the prior 12 months. In April, notable jobs gains occurred in professional and
  business services, construction, health care, and social assistance. (See table B-1.) 


On the other hand, the -103K figure comes from the household survey and reflects a shrinkage on the workforce (due to a decrease in labor force participation).


  The household survey includes agricultural
  workers, self-employed workers whose businesses
  are unincorporated, unpaid family workers, and
  private household workers among the employed.
  These groups are excluded from the establishment
  survey


Furthermore, in the latter (household) survey the number of the unemployed decreased even more by 387K. The difference between 387K and 103K is about 284K which is a good enough approximation for the 263K from the establishment survey given the different methodologies.