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As far as I know, there are several notations of equality by definition,

i.e.

$:=$, $\equiv$, $ \buildrel\triangle\over =$,$=$

What is the difference between each one?

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    There is no general answer, as this is a matter of convention. The first three emphasize that a definition is being made, whereas $=$ need not indicate that. The first is, I think, borrowed from computer science, as it is easier to typeset. The second is less common that the first and third, I would expect, in part because the notation may clash with other uses of $\equiv$. – 2017-02-19
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    I also like $\stackrel{\cdot}{=}$. – 2017-02-19

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Like @Travis said, the symbols generally depend on the context they're used in. You'd really have to look to the specific book or person using the symbol to know for sure.

That being said, in general, I've seen the symbols used like so:

$:=$ is "defined as" where you're declaring a statement $$x := y$$ means $x$ is defined as $y$, or $x$ is just another way to say $y$. Like others have said, I've usually used it in computer science, or computational mathematics applications.

$\equiv$ is "equivalent to" or congruent to, often used like so: $$x\equiv a\>\; (\text{mod} \;b)$$

$\buildrel\triangle\over =$ is "equal to by definition". I guess if you were trying to be really nitpicky, it might not technically be the same as defining the statement outright, you're just invoking the definition. But again, it depends on the application.

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    Don't forget that $\equiv$ is also some times used for _identities_, i.e. equalities that are always true. For instance, $(x-y)(x+y)\equiv x^2-y^2$. – 2017-02-19