Difference between SSM and SSR Are SSM(sum square of mean?) and SSR(sum of square due to regression) are same or they are two different things? 
 A: Actually, it is typical to label $\sum(y_i - \hat y_i)^2 = SSE$ while $\sum(\hat y_i - \bar y)^2$ is labeled either $SSR$ or $SSM$. Most sources use $\sum(y_i - \bar y)^2 = SST$, so that the decomposition of variance is generally either $SST = SSE + SSM$ or $SST = SSE + SSR$. See, for example, http://www.stat.yale.edu/Courses/1997-98/101/anovareg.htm or https://www.youtube.com/watch?v=aq8VU5KLmkY
So, the answer to your question is that $SSR$ and $SSM$ are just two common notations for the same quantity.
A: They are the same if your linear regression model only has an intercept term. Otherwise they are different. 
SSR is defined as $\sum_i (y_i - \hat{y}_i)^2$, where $\hat{y}_i = \hat{\beta}_0 + \hat{\beta}_1 x_{1,i} + \cdots + \hat{\beta}_p x_{p,i}$. 
If you only have an intercept, your model is $y_i = \beta_0 + \epsilon_i$, your estimate is $\hat{\beta}_0 = \bar{y}$, and SSR simplifies to 
$$
\sum_i (y_i - \hat{y}_i)^2 = \sum_i (y_i - \hat{\beta}_0)^2 = \sum_i (y_i - \bar{y})^2 = \text{SSM}.
$$
In general, this is always true:
$$
\sum_i (y_i - \bar{y})^2 = \sum_i (y_i - \hat{y}_i)^2 + \sum_i (\hat{y}_i - \bar{y})^2
$$
which is a famous decomposition of variance: SSM = SSR + SSE. 
