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The Progress in International Reading Literacy Study (PIRLS) is an international assessment and research project designed to measure reading achievement at the fourth-grade level, as well as school and teacher practices related to instruction.

The Trends in International Mathematics and Science Study (TIMSS) was developed by the International Association for the Evaluation of Educational Achievement (IEA) to measure trends in students' mathematics and science achievement.

TIMSS focuses on effectively measuring educational achievement in mathematics and science at the fourth and eighth grades, and sometimes the final year of secondary school. The study is designed to capture the breadth and richness of these subjects as they are taught in the participating countries.

TIMSS is intended to measure how well students have learned the mathematics and science curricula in participating countries, whereas PISA is focused on the application of knowledge to “real-world” situations.

Trends in International Mathematics and Science Study - Wikipedia.

The goal of TIMSS is to provide the best policy-relevant information to help improve mathematics and science teaching and learning. TIMSS 2019 included student, teacher, and school questionnaires and the Early Learning Survey (also called the “home questionnaire”) completed by students' parents or caregivers.

TIMSS data have been collected from students at grades 4 and 8 every 4 years since 1995, with the United States participating in every administration of TIMSS. TIMSS Advanced studies the achievement in advanced mathematics and physics of students in their final year of secondary school.

However, each assessment defines the population to which it is generalizing (and thus from which the sample is drawn) differently. One key distinction between NAEP and TIMSS, on the one hand, and PISA, on the other hand, is that NAEP and TIMSS use grade-based samples and PISA uses an age-based sample.