Malapropism fits the bill I think.

Form oxford:

The mistaken use of a word in place of a similar-sounding one, often with an amusing effect (e.g. ‘dance a flamingo’ instead of flamenco).

Origin

Mid 19th century: from the name of the character Mrs Malaprop in Sheridan's play The Rivals (1775) + -ism.

Malapropism fits the bill I think.

Form oxford:

The mistaken use of a word in place of a similar-sounding one, often with an amusing effect (e.g. ‘dance a flamingo’ instead of flamenco).

Origin

Mid 19th century: from the name of the character Mrs Malaprop in Sheridan's play The Rivals (1775) + -ism.

EDIT: I know this doesn't seem to satisfy the OP's example of bored/board. But the OP maybe couldn't think of a better example. It satisfies what they asked for in the title: "What's the term for using the wrong word because it sounds the same"