The  key difference between "job" and "work" is actually a very simple grammatical one: "job" is a countable noun while 'work" is uncountable.

The two sentences are wrong simply because the writer is trying to use an uncountable noun (work) as if it were countable.

Uncountable nouns - such as rice, advice, information or equipment - cannot take an indefinite article and cannot be used in the plural form. So you can't say "a work" and you can't say "three works". That's the only reason why they're wrong. It's just about grammar, not meaning.

By the way, Julia...did you mean to insert a mistake into the very first sentence of your post? Hint: it's the first word.

Sorry to disagree, Julia, but you are misleading your students if you are telling them that the definition of " job" is a regular activity or occupation for which you receive money. This is not the case at all. "Job" does not always have to refer to a paid position or employment.

A "job" can simply be a  task or a chore that needs to be done. If you ask your husband, for example, to prune a tree in your garden on a Sunday afternoon, this is a job. It isn't regular, it isn't his occupation, and he isn't going to be paid for it. But it's a small  job that you want him to do. If you ask him to do two more things, then you have three jobs for him to do. 

As I explained above, and Jerry has confirmed, it's a question of grammar rather than meaning. In fact, the origin of the word "job" in this sense is the now archaic phrase "a job of work". Like "a piece of advice" or "a slice of bread", the word "job" is a countable noun used to refer to an individual unit or units of a mass noun.

Good question, Julia.

Jack is correct that "job" is often the term used to refer to paid employment or occupation.

However here in the US, we also use it to refer to specific work projects even in the home. So for instance I can tell my husband, "Honey, I've got a job for you to do. How about cleaning up the garage?"

So do you see how the word ''job'' can be used? So for questions 1 and 2, the term job would apply; however, I would prefer using "tasks" in place of "job" for the garden sentence. "I have three tasks to do in the garden."

"Work" is a generic term to refer to any kind of activity that involves effort. But you can also use it in this context: "Paid work is necessary for my survival. I can't volunteer indefinitely."

A common statement is ''My job isn't work. It's play."  That obviously means that one enjoys the job (the work) because it does not appear to involve effort.

Юлия, you took a good shot at it. But I have to agree with Su.Ki. The difference really is grammatical.

In my view, as a native speaker of English, you are splitting hairs with your definitions. And not to be redundant, but your explanation is not responsive to the question that you asked.

Thanks for your explanations. As for me, I would explain the difference between these two words like that:

JOB is a regular activity that you do; an occupation, a profession. You receive money for this activity. Job is a regular NOUN.

WORK is more general then job. Work refers to the activities done to accomplish a goal. Work can be done both inside an official job and outside a job. Work can be a verb and an uncountable noun.

So, the right questions will be:

1) Do you have a full-time job?

2) I have some work to do in the garden.