Analysis of means is a graphical alternative to ANOVA that tests the equality of population means. The graph displays each factor level mean, the overall mean, and the decision limits. If a point falls outside the decision limits, then evidence exists that the factor level mean represented by that point is significantly different from the overall mean.
ANOVA tests whether the treatment means differ from each other. ANOM tests whether the treatment means differ from the overall mean (also called the grand mean).
One more important difference is that ANOVA assumes that your data follow a normal distribution, while ANOM can be used with data that follows a normal, binomial, or Poisson distribution.