You could use both to accomplish the same thing, sure. But their concepts are quite different.
Rake works on tasks, which you define (or import from some gem).
Make works with file targets more than tasks. You define how it can make a certain (type of) file and it does the job.
Personally I mostly use Make if I want to generate files from something else. Otherwise I find small scripts easier than Rake or equivalent.
make is pretty neat if you think about it as a framework to help you compute/derive values from other values. each value happens to be stored in the filesystem as a file.
in contrast, many of the newer build-tool make replacements seem to miss the whole value of values and either push or force you in a direction of doing actions with side effects.
file 'blogpost.html' # we want to produce blogpost.html
# this rule specifies how to build
# any .html from the source
rule ".html" => ".md" do |t|
sh "pandoc -o #{t.name} #{t.source}"
end