Sort of, I can speed up the healing process and make sure that you can walk tomorrow, but the leg will need time to heal properly.- Healer to a peasant with a broken leg
Magic users, especially competent ones and those who can heal are smost sought after. Some choose more destructive spells and enter military service, although this is rare.
In order to qualify as a "professional wizard" all you need is the ability to cast spells and you need to use them in service of someone, be it for money or with another motivator.
In some nations wizards are actively sought out by the government and kept away from the public. In these places wizards are more a thing of myth then actual people.
Even if the spells are limited in amount and strength, magic users can live comfortable lives while being respected by the community. The respect is in part due to fear, because commoners do not know how powerful the wizards really are.
Due to this respect many wizards live somewhat secluded and often alone with few close friends.
Many think that those who have these powers should tech them to the general population, but within the profession the consensus is that magic should be a well guarded secret. Because people are nervous about both loosing the support of the magic wielders and don't want to fight against magic, the issue has never escalated to violence.
Being able to cast spells
Payment & Reimbursement
Most wizards are payed in coin either before or after a job, but some are paid on an hourly wage. The latter are usually in some form of employment by a government.