The Difference Between有点儿 And 一点儿

有点儿/一点儿
一点儿
(1)to be used to modify noun，it should precede a noun， 一点儿+noun
eg. 1——瓶子里还剩多少牛奶？
-How much milk is left in the glass?
——只剩一点儿（牛奶）了。 P.S. The 牛奶 here it can be elided.
-A little (milk is left).
2我跑完步后喝了一点儿水。
I drank some water after running.
(2) to succeed follow a verb and or an adjective
eg. 1 今天比昨天冷一点儿。（冷 is "cold", an adjective here, it means cold.）
2 你再吃一点儿吧. (吃 is a verb, it means "to eat", a verb.)
(3) to be used use in a fixed usage “一点儿也不” 一点儿也不means “not at all”
eg. 我们坚持让他休息，但他强调他一点儿也不累.
We insisted on him having that he take a rest but he emphasized argued that he felt is not tired not at all .


有点儿
（1）to be used use to modify adjective/verb, it should precede adjective/verb, 有点儿+adjective/verb
eg.1 ——我们出去散步吧？
What How about going for a walk?
——我有点儿累，我想休息下。(累 is "tired", a verb , it means be tired)
I am a bit tired. I want to have take a rest.
2 今天有点儿冷。(冷 is "cold", an adjective here, it means cold.)
It is a bit cold today.
3我有点儿饿了。（饿 is "hunger", a verb, it means be hungry.)
I am a little hungry.
4 我有点儿想家。(想家 is "longing for home", a verb.)
5 我有点儿害怕。（害怕 is "scared", a verb.）
(2) 有+点儿，"有" is a verb，"点儿" is a classifier here. “有+点儿" is used before noun
“有+点儿” means “has/have a bit/little/some” “be a bit/little/some”
eg.1 桌子上有点儿水。
There is some water on the table.
If elided the classifier “点儿" is elided, the sentence change to becomes 桌子上有水. It is This is also grammatically correct in grammar.

今天比昨天冷一点儿。　
今天有点儿冷。
Please pay attention to the positions of 一点儿 and 有点儿 at these of the above two sentences.