adder
Synonym discussion
Sense: noun/1
In British wildlife writing, 'adder' usually means the European adder, the small venomous snake also called the common viper. 'Viper' is the broader biological label for the whole family, so every adder is a viper, but many vipers are not adders. 'Cobra' names a different kind of venomous snake with a hood and a very different body shape, so it should not be used as a synonym for adder. 'Grass snake' is another British snake, but it is non-venomous and usually slimmer and longer than an adder. If you are talking about the specific British species, choose 'adder'; if you mean the wider family, use 'viper'.
Etymology
Modern English 'adder' actually brings together two different histories. The snake word comes from Old English 'næddre', which later changed shape when speakers redivided the phrase 'a nadder' as 'an adder'. The arithmetic word is much newer: it was formed inside English from the verb 'add' plus the ending '-er', first for a person who adds and later for machines and computer parts. So the snake sense and the arithmetic senses share a spelling today, but they do not come from the same root.