On a broader scale the ITCZ and monsoons are related. This is because the global circulation shifts as a result of the tilt of the earth's axis relative to the orbit around the sun. In northern hemisphere summer, the northern hemisphere is tilted towards the sun and receives more radiation (energy) than the southern, and vice versa for northern winter, The southern hemisphere is affected in the same way. Without the tilt we would not experience any seasons.
In the tropics the largest amount of energy reaches the region where the sun is at the zenith. In northern summer this region is north of the equation, where as in winter it is at the south. At the spring and fall equinox it coincides with the equator. Hence the region of maximum energy input wanders seasonally to the north and south of the equator.
Climatologically the region with maximum energy input sets up a circulation in the form of so-called Hadley cells where warm air rises where it is heated the most and then transported at elevation to the north and south. At the location of upward air flow formation of convective clouds yielding precipitation becomes the norm. This zone to which ground winds flow towards the region of maximum energy influx is the ITCZ and because the zone of maximum solar energy influx wanders, the ITCZ flows. The zone is fairly wide so the regions around the equator sees the effects of tropical precipitation more or less without seasonality, actually two rain periods and two drier periods as the ITCZ moves once to the north and once to the south over the region each year. Away from the equator the resulting period of precipitation becomes more and more marked as one moves to the north and south resulting in strongly seasonal rains.
This movement of the large scale circulation on the earth produces several associated effects and the different monsoons are such phenomena. There are several monsoons on the earth created by weather phenomena typical for the specific region. The Asian monsoon is perhaps the most known. The specific conditions leading up to this monsoon is found in the high elevation Tibetan plateau. During the northern winter the plateau sees a larger high pressure forming which generates winds flowing south over India and causing a dry climate. During the northern summer large parts are heated generating a low pressure over land which draws in moist air from the sea yielding strong precipitation. Hence the monsoon follows the same seasonality as is seen in the wander of the ITCZ but the cause for the regional change in seasonal wind and precipitation pattern has a different cause.
So to understand the large scale weather systems and their seasonal patterns, you must start by understanding how solar energy drives the atmospheric circulation. This causes a specific and typical pattern which is locally disrupted by the distribution of land and oceans on the earth. Land masses can be heated more and more quickly than oceans on a seasonal basis, land masses also includes topography that can impede the atmospheric circulation, so it it perhaps obvious that land masses contribute on regional and local scales.