What is the difference between list.files and dir?

They are identical in the sense that they take the same arguments, these arguments have identical defaults, and they use the same .Internal function to execute.

As pointed out by @RichScriven in the comments, a compact and accurate test that they are the same can be run using identical:

identical(list.files, dir)
[1] TRUE

We can also take a look at their source code.

dir
function (path = ".", pattern = NULL, all.files = FALSE, full.names = FALSE, 
    recursive = FALSE, ignore.case = FALSE, include.dirs = FALSE, 
    no.. = FALSE) 
.Internal(list.files(path, pattern, all.files, full.names, recursive, 
    ignore.case, include.dirs, no..))
<bytecode: 0x000000000fe1c388>
<environment: namespace:base>

and

list.files
function (path = ".", pattern = NULL, all.files = FALSE, full.names = FALSE, 
    recursive = FALSE, ignore.case = FALSE, include.dirs = FALSE, 
    no.. = FALSE) 
.Internal(list.files(path, pattern, all.files, full.names, recursive, 
    ignore.case, include.dirs, no..))
<bytecode: 0x0000000008811280>
<environment: namespace:base>

Note that

.Internal(list.files(path, pattern, all.files, full.names, recursive, 
        ignore.case, include.dirs, no..))

is executed in both functions.