I have some question about the difference between the verb "break" and the verb phrase "break off" in these contexts:
1a. He broke ties with terrorist groups.
1b. He broke off ties with terrorist groups.2a. America broke diplomatic relations with Cuba.
2b. America broke off diplomatic relations with Cuba.
Are "break" and "break off" the same in those two sentences, or are they subtly different?
They are very similar in meaning in the contexts you have provided, so in my understanding the difference of which verb choice to make is a stylistic one, and has to do with common usage.
"break off" is used when you talk about discontinuing a relationship of some sort, as in "break off diplomatic relations": http://www.merriam-webster.com/dictionary/break%20off In your example, I think "America broke diplomatic relations..." sounds a bit out of place, unless it's being used in a comedic sense (as in causing something to be broken).
Similarly, "to break ties" is an expression in common usage. You could probably say "to break off ties" and it might imply that the ties were broken suddenly.
In general you'll find that phrasal verbs which are synonymous with other verbs differ primarily in the contexts where they are used, so that inserting one of the synonyms wouldn't be technically wrong, but it wouldn't sound "natural".
In both instances, "broke off" is the more idiomatic usage. One could say "break ties" but one would not say "break relations".
See also J.R.'s link.
If you and your SO have a "break-up", then your relationship could be said to be "broken", but you wouldn't say that either of you "broke" it. If you were married, and she leaves, and leaves you with a kid to raise, one might have said the kid is growing up "in a broken home" (the politically correct term is now "in a single-parent family").
When you want to end a relation or connection with somebody, you can use either the verb break or the phrasal verb break off, with the subltle difference that you use the "break off" when you end the relation suddenly. Oxford Learner's Dictionary and The Free Dictionary say that break off means to disctontue or end suddenly.
