According to the author, when we focus on student achievement and making comparisons among students or comparisons to a criteria, we are sorting and selecting talent. We do this so that we can identify excellent performance in contrast to poor performance. This type of grading typically results in a percent or letter that means anything from excellent to failing.
However, if we focus on effort, behavior, and growth, then our interest is clearly in developing talent and assisting students to learn. We do this so that we can identify change in learning over time. This type of grading typically results in anecdotal records and portfolios of student work that demonstrate effort and improvement.
Despite the obvious bias against grading achievement, I think the descriptions of the two approaches are useful. However, I do object to the basic premise that there are only two purposes to grading. I would like to propose another perspective. I believe that the primary purpose for "grading" (as opposed to "assessment") is the need to report. If no one outside the classroom had any interest in how much, how fast, or how well a student has learned, there would be no need for grades. Teachers could simply assess learning and make instructional decisions based on the results. However, parents in particular want (and have the right) to know the answer to one very important question, "How is my child doing?" By this they mean, "Is s/he making age-appropriate progress in learning concepts and developing skills?" It's a simple question, but it is absolutely crucial to every parent.
There are others who also need this information. The school and district administrations want to know how well their programs are working. They want to know how well their teachers are delivering the curriculum. They want (and have the right) to know that their employees are doing a good job, and the only valid measure of that is student learning. They too will need some kind of report.
State and federal governments and the public in general also want to know how their schools are performing. They have a right to know whether taxpayer dollars are being well spent. They need to know where to target new money and where to make cuts when times are tight. They too will need some kind of report.
Once we understand that others outside of the classroom need a report about learning, then we are ready to grapple with the many issues related to grading. We also will immediately see that anecdotal records and portfolios of student work alone are inadequate for the kinds of reports that are needed. For additional thoughts on reporting see here.