Context and coercion

[Joshua Choi]

Kudos to all on the Perl 6 mailing list,

What's the conceptual difference (or relationship) between context and type
coercion? Is
    $moose.prefix:<~>
the same as
    $moose.coerce:<as>(Str)
for instance?

And forgive my brain, but how would you nicely define coercion in a class?
Like, could you spare an example?

Also, what's the point of making a whole grammatical category for "coerce"
that behaves like an infix operator?

Thanks in advance.