As a non-expert, allow me to offer the following definition(s) and types of assessment as I see it.
Formative assessments are used while students are learning new content (e.g. use of Clickers, mastery quizzes with multiple attempts), while summative assessments evaluate mastery of few chapters. Low stakes assessments are used to evaluate students learning and gaps (one-minute papers, breakout rooms in online synchronous classes, and think-pair-share), while high stakes are the major tests/exams or Lab Practical Final. To me it's important that all kinds of assessments give me feedback which I can in turn use to review and discuss with students for their learning improvement. One can do it even with high stakes exams, and if a question has been answered incorrectly by most students, then perhaps I need to review it and figure out a different and/or supplemental way of teaching the concept for that group of students. As I have progressed in my over 30-years of teaching, I shifted from only summative, high-stakes assessments to regularly using low-stakes and formative assessments.