A suspended sentence is breached if the offender commits any further offence before the end of the suspended sentence. It can result in the suspended sentence being activated but it's not automatic.
For example, if someone was sentenced to 12 months imprisonment for burglary, suspended for a year, and then he committed a further offence of theft during that year, it's likely that the suspended sentence would be activated by the court (plus, of course, an additional sentence for the second offence).
However if the person, referred to above, committed an unrelated crime during the period of his suspended sentence (e.g. drink-driving) the court might decide not to activate the suspended sentence (although it could do so).
A supervision order (= 'probation') is breached if an offender fails to comply with any of the terms of the order (or of any reasonable conditions imposed by the probation service under that order). So simply arriving late for a probation appointment could be a breach.
For a single minor breach of a supervision order (e.g. missing an appointment or arriving very late), the probation service will send the offender a warning letter. A second minor breach (or a single breach deemed to be 'serious') will result in the probation service referring the matter back to court. If this happens, the court is obliged to impose an additional punishment (such as unpaid work) or substitute a different sentence (such as imprisonment).
Chris