Plain English Meaning
These are the FAA's official rulebooks that say exactly what you need to know and do to pass your pilot tests. The PTS is the older version. The ACS is the newer version that has mostly replaced it, and it adds knowledge and risk-management items alongside the flying skills.
Full Definition
The official FAA documents that specify what an applicant must know, consider, and be able to do to pass a knowledge test and practical test (checkride) for a pilot certificate or rating. The Practical Test Standards (PTS) was the older format, listing required tasks with specific performance tolerances. The Airman Certification Standards (ACS) is the newer, expanded format that replaces PTS for most certificates and ratings; it integrates knowledge, , and skill elements into a single for each . Together, ACS and PTS define the an examiner uses to an applicant.