xiao de, means the small one ( something you know under certain context). so , you see, xiao de seems to work as a noun. while " xiao" is just small. used to describe the size of something. as an aside, " xiao de" is a devaluing or debasing way of addressing yourself to someone superior to show respect in ancient Chinese. you may correct my English :)

no difference between 小 and 小的in the meaning,however, there is a little difference in the usage, such as 小孩 is right, 小的孩 is wrong, both小手套and 小的手套 are right,穿小鞋 is right，穿小的鞋is wrong，otherwise you can think that 穿小鞋is a meaning, 穿小的鞋 is another meaning, these are only a habit.

小 = small, little 小的 = the smallness of... In ancient time, 小的 can also mean "I" to indicate the lower status of the speaker. Chinese like to use the 3rd person to indicate politeness.