What are the main differences between R data files?

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:

The difference is not about the compression, but serialization (See this page)

Like shown in the manual page, you may wanna use it to restore a certain object with a different name, for instance.

You may readRDS() and save(), or load() and saveRDS() selectively.

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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

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