Rda is just a short name for RData. You can just save(), load(), attach(), etc. just like you do with RData.
Rds stores a single R object. Yet, beyond that simple explanation, there are several differences from a "standard" storage. Probably this R-manual Link to readRDS() function clarifies such distinctions sufficiently.
So, answering your questions:
In addition to @KenM's answer, another important distinction is that, when loading in a saved object, you can assign the contents of an Rds file. Not so for Rda
> x <- 1:5
> save(x, file="x.Rda")
> saveRDS(x, file="x.Rds")
> rm(x)
## ASSIGN USING readRDS
> new_x1 <- readRDS("x.Rds")
> new_x1
[1] 1 2 3 4 5
## 'ASSIGN' USING load -- note the result
> new_x2 <- load("x.Rda")
loading in to <environment: R_GlobalEnv>
> new_x2
[1] "x"
# NOTE: `load()` simply returns the name of the objects loaded. Not the values.
> x
[1] 1 2 3 4 5
Source: Stackoverflow.com