Breach, break, split, schism, rent, rupture, rift are comparable when they mean a pulling apart in relations or in connections.
Breach, the most general in application of any of these terms, is capable of being referred to any such pulling apart without in itself, as apart from the context, throwing light on its cause, its magnitude, or its seriousness.
Break (see also BREAK n) is often substituted for breach when one wishes to emphasize the strain that is inducing or has induced a disruption (as between persons or groups).
Split usually implies a complete breach, suggesting a division such as would be made by an ax or knife; often, also, it hints at the impossibility of bringing together again the two parts (as parties or factions) that once formed a whole.
Split often implies a division of friends or friendly groups into opposing parties or factions.
Schism implies a clear-cut separation between divisions of an original group and consequent discord and dissension between the two parts; typically the term is used of such a division in a religious communion, but it may be applied to any union of rational beings (as a political party or a philosophical school).
Rent suggests an opening made by tearing or rending and may impute characteristics (as irregularity, jaggedness, and narrowness) to a break to which it is applied.
Rupture approaches breach in meaning, but it carries a more clearly defined stress upon a break in relations between people or groups; in addition, it frequently is affected by its special medical use and then often suggests an actual but not always clearly apparent break.
Rift implies a breach that is made usually by some natural process (as one that produces a separation of rocks in a mountain or a cracking of the earth); consequently it is often applied to a breach that is small at first and is in danger of growing larger.