There are big differences. Albert gave the definition, which then translate into effects. The effects of intense precipitation is that the soil (or other substrate) becomes saturated, and the infiltration rate is exceeded. This leads to a greater percentage of the total precipitation contributing to runoff and creating, for example, more flash flood.
It is easy to visualize the difference of rain intensity. Over a hypothetical year you could have 365 cm of rain. Just imagine the difference of having all that rain on one day and 364 sunny days, vs having just 1 cm of rain a day.
Likewise it is easy to visualize the difference of a higher precipitation....1 cm each day vs 2 cm each day.
The combination of rainfall amount and intensity starts to get more interesting. :)
There are lots of good, old publications on this work. Google scholar search for "precipitation intensity runoff"