1、两者中文意思不一样：
no more than表示只是，至多，只不过的意思。
not more than表示至多、仅仅、不超过的意思。
2、两者用法不一样：
no more than 表示“只不过”(= only)，强调少。
例如：She is no more than an ordinary girl。她只不过是个普通的女孩。
not more than 指两者虽然都具有某种特征，但程度不一样，意为“不如”、“不及”。
例如：He is no more a writer than a painter。他不是画家，也不是作家(= He is neither a painter nor awriter)。
3、两者词性不一样：
no more than是副词。
not more than是名词。
参考资料：百度百科-more than
1. no more than的意思是“仅仅”“只有”“最多不超过”，强调少。如：
This test takes no more than thirty minutes.
这个测验只要30分钟。
The pub was no more than half full.
该酒吧的上座率最多不超过五成。
For thirty years，he had done no more than he（had）
needed to.
30年来，他只干了他需要干的工作。
2. not more than为more than（多于）的否定式，其意为不多于 ”“不超过 ”
。如：
Not more than 10 guests came to her birthday party.
来参加她的生日宴会的客人不超过十人。
也许你看了解释还不太清楚，下面有具体比较的例子，你可以看看，看了之后也许你就懂了。
比较：
She has no more than three hats.
她只有3顶帽子。（太少了）
She has not more than three hats.
她至多有3顶帽子。（也许不到3顶帽子）
I have no more than five yuan in my pocket.
我口袋里的钱最多不过5元。（言其少）
I have not more than five yuan in my pocket.
我口袋里的钱不多于5元。（也许不到5元）
than ten tickles left.剩下不到十张票.(有“票少”的含义) The experiment was done by not
more than 5 persons.做这个试验的人不到五个.(没有“多”或“少”的含义,只是客观地说明数目) This room is
no bigger than that.这个房间并不比那个大.(有“两个房间都不大”的含义) This room is not bigger
than that one.这个房间不比那个大.(没有“两个房间都不大或都不小”的含义) [注]注意not ….Any more than或no
more...than在下面句子中的用法.如：They cannot do the impossible any more than we
can.他们和我们同样不能做不可能的事情.He is no more diligent than I am.他和我同样不勤奋本回答被提问者采纳
He is no more than an ordinary English teacher. 他只不过是个普通的英文老师。
He has no more than three children. 他只有 3 个孩子。
He has not more than three children. 他最多 3 个孩子(有或许还不到 3 个之意)。
2. 用于比较两件事物时，no more ... than 表示对两者都否定，意为同……一样不(＝neither ... nor)；而 not more ... than 指两者虽都具有某种特征，但程度不同，意为不如、不及(= not so ... as)。如：
He is no more a writer than a painter. 他不是画家，也不是作家(= He is neither a painter nor a writer)。
A whale is no more a fish than a horse is. 马不是鱼，鲸也不是鱼(=Neither a horse nor a whale is a fish)。
She is not more clever than he is. 她不如他聪明(= She is not so clever as he is)。
Each class has no more than 8 students.
每个班级的学生不超过8个.
Most molecules live for no more than weeks at a time.
要知道大多数分子的寿命都不超过一星期.
The American Heart Association advises no more than 3 grams for healthy people.
美国心脏协会建议,对健康人来说,每天食盐不应超过3克.
以上,都有"只不过/仅仅"强调很少的意思.
not more than 就没有"很少"这种意思.只是客观上说,不多于...
not more than不超过；至多；不比…更…
And the earholes are not more than three.
还有耳洞不能超过三个.
Answer these questions in not more than 75 words.
回答以下问题,不要超过75个单词.
I have not more than three relatives in this city.
在这个城里,我至多只有三个亲戚.