By vs. Until

Both words until and by indicate “any time before, but not later than.”

By
By is used in both positive and negative sentences.it is used with verbs referring to one action performed at a specific point of time like:return,pay,finish,end,arrive,...

By in positive sentences

By indicates a deadline and means that an event ,situation or state :

A- does not continue later than a particular time and it happens at or before that time.
- I will return your camera by Friday.
- He left his office by 4 o'clock.
- The train is due to arrive by 9 o'clock.
- We will finish our report by tomorrow.

B- Happen during a period of time.
- We danced by midnight.
- By noon,many people had visited the museum.

By in negative sentences

By in these kinds of sentences is usually used when something is later than than expected.

Until
Until can be used in both positive and negative statements.In positive sentences it means "up to the time of" and in negative contexts it means "at a specified time".
Until is used with verbs showing continuous states or situations like: continue, wait, drive, walk, live,...

Until in positive statements
In these sentences until:
A- emphasizes the amount of time that is left before a certain time:

- We have until 8'oclock to finish the report.
- She has until Friday to deliver her documents.

B- means an event or state that continues to a specified time in the future and then stops:

- We slept until noon.(we slept up to the noon not later)
- They danced until midnight.
- The ticket is valid until March.(it is valid up to March and not latter than it)
- We waited until the rain stopped.
- She didn't come back until the evening.

Until in negative statements

Not until is used to highlight that an event must not happen or become possible before a specified moment in time or before something else has happened but it happens at a particular time or date. As a summary, we can use until in negative statements when something is later than expected,not before a specific time or event.If until is used in negative sentences, it announces a deadline.

- If we don't arrive until five we are late.(if we don't arrive at five OR anytime till five)
- We didn't sleep until noon.(We slept at noon)
- The ticket is not valid until March.(the ticket becomes valid on the first day of March)
- We didn't wait until the rain stopped.(we moved out when it was still raining.)
- She didn't come back until evening.( not anytime before evening but at the evening)
- He won't be back until 7 o'clock.( He will be back at 7 o'clock)

Common errors
Note the following sentences:
- Until the train got into the station, we had been waiting for six hours. (incorrect)
- By the time the train got into the station, we had been waiting for six hours. (correct)

By the time is not compatible with never:
- The baby never slept by the time her mother arrived. (incorrect)

-The baby never slept until her mother arrived . (correct)

References:
Grammar exchange.com
English forums.com

When vs. By the time

When and By the time are both two time adverbs which there is a slight difference between them.
The former implies " simultaneity,at the moment " but the latter would mean that one event has been completed before another .

- She was cooking the food when we returned house.
- She had cooked the food by the time we returned the house.

In the second sentence, the cooking had been done at some point before she returned.
Notice that by the time can not be replaced with when or vice versa .

In time vs. On time

The difference between "in time" and "on time" sometimes is blurred.
In time indicates that you have arrived for a particular event early or soon enough to do something.Before the last moment.In time usually comes with" just".

- He arrived just in time for dinner.
- If I didn't hurry up, I wouldn't be in time to get to work.
- If I hadn't arrived in time , she would have killed herself.

On time indicates that you arrived somewhere at the appointed time and not late or not early.It sometimes comes with" right".

- In japan, trains are always on time.
- I may be up watching T.V until midnight ,but I am always on time for my work.
- The conference ended just right on time.

To understand better the difference between the two, notice the following sentences:

- The exam will begin on time. If you want to be calm and without stress you should attend the school in time .
- Trains in this country depart the station on time.If you want to catch the train ,you must arrive in time.