What's the difference between 一份工作 and 一家工作? I just encountered in the HSK4 book 一份工作 while I'm accustomed to 一家工作.  Judging from Baidu (一份工作; 一家工作), both are grammatically correct and widely used.

I am unsure if they're different or not.  My guess in this case is that they're the same, but sometimes the measure word changes the meaning.

Question: What's the difference between 一份工作 and 一家工作?
The correct measure word for 工作 is 份, so 一份工作 is correct. 

一家工作 you linked in is shorthand for 一家公司工作. In spoken, you might hear one say 我在这一家工作了很久 == 我在这一家公司/单位工作了很久.