It's my understanding that the MH90 tire has a higher load rating than the 90/90. If you go to the manufacturers web site you should be able to find a chart listing their tires and weight ratings so you can confirm this for yourself.
MH90 is the same thing as 80/90. MJ90 is equivalent to 90/90. MM90 is 100/90. Just a different way to show the size.
The first number in 90/90 means approximately 90 centimeters wide, section width (they do vary, though). The second 90 means the sidewall height, bead to pavement, is 90% of the section width. So a 90/90 tire would be approx 90cm wide and 81cm from pavement to tire bead.