Use of and operators in R

Question

A little bit of trouble getting hold of what are the $ and %% terms.

As I understand I can use the $ term to pull a certain value from a function (e.g. t.test(x)$p.value), but I'm not sure if this is a universal definition. I also know it is possible to use this to specify to pull certain data.

I also want to know about the use of the %% term, in particular, if I am placing a value in between it (e.g. %x%) I am aware of using it as a modulator or remainder e.g. 7 %% 5 returns 2. Perhaps I am being ignorant and this is not real?