what is the different??

(1) The homework is to be finished by student.
(2) The homework is finished by student.

The sentences are in passive voice 被動語態. Let's change them to active voice before explaining the difference. Also, consider to change "student" into plural forms "students" to express all the students in general, or "the students" to refer to some specific students.

(1) The students are to finish the homework.
(2) The students finish the homework.

"are" in sentence (1) is classified as auxiliary verb 助動詞。

"be' 助動詞 + infinitive 不定式 具有至少兩個特殊用途和意思。

根據 Oxford 字典： "be to do something"
1- used to say what must or should be done
2- used to say what is arranged to happen

所以，第一句話是說：學生應該或按照安排 去做出 "finish"作業 這個動作。

然而，第二句是只一般性 "現在時態" 的敘述，說：學生習慣性地 (habitually) 去做出 "finish" 這個動作，或作一種事實(factual)的陳述。但是，在意義上有不足之處。"現在時態" 說 "finish" 這動詞 是比較難理解。

用 present perfect tense 將會比較常見：
~ The students have (already) finished the homework.
~ The homework has (already) been finished by the students.

或者，用 simple past tense ：
~ The homework was finished by the students.

2014-08-12 14:40:06 補充：
或者，用 simple present tense to write rules and regulations：
Example:
Academic performance cannot be measured until the homework is finished by the students.

2014-08-12 23:42:29 補充：
To tell the "purpose" or to emphasize the "use" of something, apart from using adverbial infinitive phrase, we would use the preposition "for" as well.

~ The homework is for the students to finish.

~ The picture is for us to give to the guests.
~ (or, simply) The picture is for the guests.

'The homework is to be finished by student.'

It is telling u the purpose of the homework as there is the use of 'to be'

This sentence empahsises more on the purpose of the homework or the one who finishes the homework.

e.g. The picture is to be given to the guests. (empahsises that the use of the picture)

--------------------------------------------------------------------------------------------------------------

'The homework is finished by student.'

This is just a statement stating an action which is a student finishes the homework.
There is no emphasis on anything but just a statement.

Difference 名詞 (noun)
Different 形容詞 (adjective)

The homework is to be finished by student
那份功課是讓學生去完成的。〔句子沒說明功課已做完。〕

The homework is finished by student.
那份功課已經被學生完成。〔句子說明了功課已做完。〕