What is the difference between curl and wget?

The main differences are:

• wget's major strong side compared to curl is its ability to download recursively.
• wget is command line only. There's no lib or anything, but curl's features are powered by libcurl.
• curl supports FTP, FTPS, HTTP, HTTPS, SCP, SFTP, TFTP, TELNET, DICT, LDAP, LDAPS, FILE, POP3, IMAP, SMTP, RTMP and RTSP. wget supports HTTP, HTTPS and FTP.
• curl builds and runs on more platforms than wget.
• wget is released under a free software copyleft license (the GNU GPL). curl is released under a free software permissive license (a MIT derivate).
• curl offers upload and sending capabilities. wget only offers plain HTTP POST support.

You can see more details at the following link:

curl vs Wget

They were made for different purposes

• wget is a tool to download files from servers
• curl is a tool that let's you exchange requests/responses with a server

wget

Wget solely lets you download files from an HTTP/HTTPS or FTP server. You give it a link and it automatically downloads the file where the link points to. It builds the request automatically.

curl

Curl in contrast to wget lets you build the request as you wish. Combine that with the plethora of protocols supported - FTP, FTPS, Gopher, HTTP, HTTPS, SCP, SFTP, TFTP, Telnet, DICT, LDAP, LDAPS, IMAP, POP3, SMTP, RTSP and URI - and you get an amazing debugging tool (for testing protocols, testing server configurations, etc.).

As many already mentioned you can download a file with curl. True, but that is just an "extra". In practice, use CURL when you want to download a file via a protocol that wget doesn't support.

Actually, the major difference is that curl includes a library (libcurl), and that library is widely used by other applications. wget is standalone.