Yes, this class of web vulnerability is called Cross-Site Request Forgery or CSRF (https://www.owasp.org/index.php/Cross-Site_Request_Forgery_%...). The Same Origin Policy (SOP) prevents one domain from receiving the HTTP responses for requests it sends to other domains. As you suggest however, the request itself can sometimes be enough to cause adverse side effects on the target server (that may be beneficial to an attacker).

It continues to be a common security issue among web applications and is why all sensitive actions should be protected with unique anti-CSRF tokens (most good development frameworks provide support for this).

If you need to relax SOP restrictions between sites you control, the modern and recommended way is via Cross Origin Resource Sharing or CORS (https://developer.mozilla.org/en-US/docs/Web/HTTP/Access_con...).