The official definition of calibration comes from the International Vocabulary of Metrology, generally known as VIM. Currently on version 3, but those who are interested are lucky as there is a consultation on going over the next version and you can download this for free from the BIPM website;
https://www.bipm.org/documents/20126/54295284/VIM4_CD_210111c.pdf/a57419b7-790f-2cca-f7c9-25d54d049bf6The official definition (section 5.18 on page 39 of the document above), is quite wordy, but it basically means that the term 'calibration' is indeed comparison of an instrument to a known standard, traceable to an official reference.
Calibration labs and manufacturers will differ though. Some calibration labs will provide a form up front for you to select the services you require, which can be either 'calibration' or 'calibration and adjustment' with before and after values or just after adjustment values. Those that do not offer this, in my country, you can be certain that 'calibration' is just checking and no adjustment is made.
Some of the more expensive apparatus that I have, the manufacturers do automatically adjust the instrument to the best performance they can get, it is quite rare for that to be done automatically though and it is always stated up front that they do this. It also comes with a hefty price tag.