Q: within-subject ANOVA with 1 subject vs. 1-way ANOVA

#1
Hello people.

I became curious if there is any difference between:

1-way ANOVA in a single subject for 3 conditions, 5 reps.
vs.
within-subject ANOVA in a single subject for 3 conditions, 5 reps.

That is, if there is only one subject, is within-subject ANOVA the same as just usual ANOVA?


Another related question is, how is within-subject 1-way ANOVA different from simple 2-way ANOVA? It seems like within-subject 1-way ANOVA controls across-subject variation first and then perform 1-way ANOVA, whereas 2-way ANOVA do not control one factor before testing difference of mean of the other factor. Is this right?

Thank you.