I suspect you’re asking about BrE, but I’ll address AmE here for completeness since the usage seems to be quite different.
In AmE, “leave” or “a leave of absence” is only used for extended periods, typically without pay unlike “sick days” or “vacation”. This must be requested in advance. If you don’t show up to work for a week or more without any contact, you will typically be fired in absentia, so requesting leave afterward is not a possibility.
Some requests for leave cannot be denied, such as family leave (which includes what was formerly called maternity leave), medical leave and military leave; employees are required by law to grant these and hold your job for your return, but you still have to formally request them before you go for those protections to apply.
Other requests for leave, such as “personal leave” or a sabbatical, are at the employer’a discretion, and they typically will not grant these requests unless you make them far enough in advance that they can arrange for someone else to cover your work.
The last category is “administrative leave”, which is due to a policy that prohibits you from doing your job while an investigation is underway, and does include pay since you are presumed innocent. For instance, after a police shooting, the officers involved will be placed on administrative leave while the shooting is investigated.