The advantage of repeated measures

The difference between ordinary and repeated measures ANOVA, is similar to the difference between unpaired and paired t tests. See the advantages of pairing or matching. Since each participant or experiment acts as its own control, repeated measures design can do a better job of separating signal from noise, so this design usually has more power. Some participants may have larger measurements at all time points, and others may have lower measurements at all time points. Repeated measures ANOVA focuses on how much the Y value changes between treatments.

Repeated measures or randomized block?

The term repeated measures is used when you give treatments repeatedly to each animal or participant.

The term randomized block is used when you randomly assign treatments within each group (block) of matched subjects.

Imagine that you compare three different treatments. In a repeated measures design, you'd recruit say 10 subjects (or use ten animals) and measure each of the subjects (animals) after each of the treatments. With a randomized block design, you'd recruit ten sets of four subject each, matched for age, gender etc. (or ten sets of four animals, with the four treated at the same time in adjacent cages...).

ANOVA works identically for repeated-measures and randomized block experiments, and Prism always uses the term repeated-measures.

One way? Or two way?

A design with three or more measurements on the same subject is called repeated measures one-way ANOVA in Prism, because there really is only one factor, denoted by the data set columns. But you could argue there is a second factor too, subject, because each row represents a different subject (or block). In fact, you'll get the same results if you analyze with two-way ANOVA (without replicates) and one-way repeated measures ANOVA.