Either curl or wget can be used in this case. All 3 of these commands do the same thing, downloading the file at http://path/to/file.txt and saving it locally into "my_file.txt":
wget http://path/to/file.txt -O my_file.txt # my favorite--it has a progress bar
curl http://path/to/file.txt -o my_file.txt
curl http://path/to/file.txt > my_file.txt
Notice the first one's -O is the capital letter "O".
The nice thing about the wget command is it shows a nice progress bar.
You can prove the files downloaded by each of the 3 techniques above are exactly identical by comparing their sha512 hashes. Running sha512sum my_file.txt after running each of the commands above, and comparing the results, reveals all 3 files to have the exact same sha hashes (sha sums), meaning the files are exactly identical, byte-for-byte.
See also: How to capture cURL output to a file?