The term “blues” in each expression means the same. It is sadness, coupled with some lethargy. In fact this answer from yahoo.com (What is the meaning of monday blues?) contains a very good explanation, and it summarizes Monday Blues as
“To put all these together, we can define MONDAY BLUES as: The low-spirited, cool, annoyed, sad, unlucky mood of those workers, students, or employees who feel that a mundane, difficult, unexpected Weekday is arriving to force them into going back to work, killing their joys and annoying them.”
Except that I would take out “unexpected” from that list.
The main meaning of blues is sadness, or expressing sadness. Not laziness. But sadness, or feeling really blue, contains an element not of laziness but lethargy, or lack of energy.
This is true whether it is Monday Blues or Morning Blues.
In fact, if you say that someone has got the blues, it means he is sad or moody or depressed.
If you feel only laziness, you do not have the blues!