(1)advancement  含有是客观的原因导致的 前进/进步/晋升

He cared little for social advancement. 

他不太在意社会地位的提升。

her work for the advancement of the status of women. 

她为提高妇女地位所作的工作

This is an inexorable law governing social advancement.
这是社会前进的必然规律。

Her rapid advancement in the scientific field is very admirable.
她在科学领域取得的飞速进步是十分令人钦佩的。

The advancement of society is just a process of innovation.
社会的进步正是一个求新的过程。

The job offers good opportunities for advancement.
这份工作有很好的晋升机会。

His advancement to the position of manager was greeted with enthusiasm.
他被提升为经理，大家都为之欢呼。

(2)advance 含有主观原因导致，尤其指空间或时间“在前面”或“向前进”。

Advance in the jungle was very slow.
在丛林中行进很慢。

Air safety has not improved since the dramatic advances of the 1970s.

航空安全自从20世纪70年代得到显著提高之后，至今再没有任何改善。

Their progress at work was mirrored by their children's educational advance. 子女在学业上有所进步，他们在工作上也就会有所起色。

This could be an advance on the present situation. 

这样可能会改善当前状况。

She asked for an advance on her salary.
她请求预支薪水。