Is there any difference between "anyway" and "either way"?

Either way means ''one way or another'' whilst anyway sounds more like you're concluding that thought.

Hope that helps.

Or think of it this way:

Choosing between two options: You can do that either way. (This way or that way)
Choosing between many options: You can do that any way you want. (many ways)

There is a difference between "anyway" and "any way":

He was advised not to [go], but he went anyway. = Aconselharam ele contra, mas ele foi de qualquer maneira.
Anyway, it was a bad choice. = Seja lá como for / Conclusão, foi uma má decisão.

Take any way you want. = Escolha qualquer caminho que quiseres.
There is only one way home; any other way will not work. = Só hó um caminho para casa; qualquer outro não dará certo.

Thanks you for helping me guys and increasing the question I have a doubt (one thing related to it), what do you think about the difference (If there's one) in the usages bellow

It was an experience that neither of us will ever forget
It was an experience that none of us will ever forget