In season 3 of the anime Eraserhead tells the students if they are going to give an exam for obtainig a semi pro license. What's the difference between a semi pro license and a pro license? What are the students who approves going to be allowed to do and what not?
The answer will be based on my interpretation.
Personally, I'd like to think of the hero licenses like driving license.
For the context, a person with a learner's they can only drive under certain condition, whereas a person with a driving license can drive a car regardless with or without permission.
Thus, a hero with semi-pro hero license can take action to be a hero in an emergency situation if the situation permits, such as if there are no pro hero(es) nearby, or to provide on-site assistance. If they don't even have this license, by their law, they're not supposed to perform any hero activities (This should make sense, else why have a license in the first place - There has to be some sort of legal constraint for them to not be able to use their quirks if they don't have a hero license). To add on, I think that if there are pro heroes on site, they shouldn't be able to freely execute any hero duties unless permitted by the pro hero. (By law, if they don't have this semi-pro license, they should leave as soon as possible from the site of danger)
Whereas, if a hero has a pro hero license, then they can (by law) perform any sort of hero activities, regardless the situation.
Besides that, another possible reason is the difference in how long their hero license could last. I wasn't able to find an image of a pro hero license, but we do have Midoriya's semi-pro hero license:
At the last line of the image, there is a line which translates to: "You can use this card till ...." Thus, I believe it is a rather safe assumption to say that their card should expire much faster compared to a pro hero's license (Similar to learner's license and driving license expiry timing as well).