Similarities between connectives 就 and 而?
Actually, these two words are very different, and it's the difference - not the similarity - you need to grasp. 

Both of these words indicate a rhetorical "following from," but 就 means "to follow from" in the broadest, simplest sense, rather like an English "then": 

When it's used as a 'verb', it's intended to show that one thing follows as a consequence of another. An excellent example of how this usage can be precisely mapped in English is below:

"若這樣就那樣“ - "If this, then that."
"他吃了整之火雞，那他就飽了。“ - "He ate the whole turkey, so he, then, [is] full!"

As you can see, "就“ as a "verb" is easily understandable as an English "then", as well. 

Now consider this:

"我渴死了“  - "I'm thirsty!"
”那，你就去喝水吧!“ - "So go drink, then...."

The many instances this phrase can be used - whether humorously, as a reprimand, as an exclamation, as an acquiescence, as mockery - all pretty much depend on "就" being the simplest, most common-sense idea anyone could have. 若一就二 - like that.

“而” is more like an "and" than a "then" - however, it is more specific and narrow because it further indicates transcendence, or moving beyond the expectations of discourse. In that sense, it's much more like "moreover" - so whether one uses it as "and," "also," "but," "however," or any other sense, it always has that meaning of saying "moreover" behind it - 

"我吃飽了，而吃太飽雅。。。“ -
"I ate, moreover {but/also/however}, i ate too much."

男： “昨晚我們去看弟弟演一出布萊希特戲..."
女： "而他演的好好看啦！“

Guy:  "Last night we went to see my little brother act in one of Brecht's plays."
Gal:  "Moreover {And/But/Also} he really acted so well in it!"

In that exchange above, "而“　can be used to indicate a "but" - 

Guy: "We went to see my brother act [implied: and i expected him to be awful]...."
Gal:  "But he really looked great up there!"

Or an "and" that draws attention to the importance of what comes after, in contrast to what came before: 

Guy: "We saw my brother..."
Gal: "And it was amazing!"

Generally, in modern Chinese it's going to indicate a "moreover" of some sort - but depending on the rhetorical context, it can be translated into other languages in any of many ways.