They mean the same thing: consisting of three parts or things, three in number, three times an amount.
A treble is also a singer with a soprano voice, often a choirboy, or a musical instrument in a high key.
In the number-related sense, treble and triple can both can be verbs, nouns, adjectives or adverbs.
Readers of Private Eye may recall the frequent cry of ‘Trebles all round!’ in the ‘Corporation Street’ series (a satire on the BBC), meaning triple measures of spirits.
Treble seems to be more common in Britain – but has a strange persistence in North American legal usage.
This is thanks to old statutory drafting in the United States, which provides in certain circumstances for treble damages. That is, an award of damages that is three times what the trier of fact determines.
Examples are found in the Clayton Antitrust Act, RICO and Title 35 of the US Code (patents).
There are frequent instances in historical Canadian legislation, although the concept does still appear in the Distress Act and Sheriffs Act currently in force in Manitoba.
Federal fisheries regulations also refer to ‘double or treble hooks’ (see Maritime Provinces Fishery Regulations, SOR/93-55, s 1(1) (‘hook’))
In the damages sense, treble actually appears to be more common in Canadian case law (some of it fairly recent) than triple (75 hits in CanLII for treble damages, 33 for triple damages).
Take your pick, but unless your statute specifies treble, I’d go with triple.