Intrinsic rewards are always non-financial, while extrinsic rewards can be financial or non-financial. Both have their value in the workplace. And certainly, each has some advantages and disadvantages.
Intrinsic rewards are those that allow employees to take satisfaction in a job well done. We provide this with challenges such as problem-solving opportunities, cross-training, or increased autonomy. This is an excellent way to motivate people, as many employees welcome and appreciate a challenge. This is also, I should add, classic Theory Y motivation, assuming that people value this kind of intrinsic reward. And that leads to the possible disadvantages. If this assumption is incorrect, for example, for an employee who seeks to only do the work, collect a paycheck, and go home, this sort of motivation is not going to work. Another disadvantage is that no matter how much internal satisfaction people get from being challenged, there can come a point at which they can start to feel they are being taken advantage of and want some external and usually monetary form of compensation. A manager who relies solely on intrinsic rewards to motivate employees is likely to create at least a few disgruntled attitudes in the long run.
Extrinsic rewards can be monetary or non-monetary. Bonuses and pay raises are rewards that are monetary. Providing extra paid leave is actually a monetary reward, too, since it costs the company money and pays the worker for not working. Other benefits that are monetary in nature are health insurance, disability insurance, and paid parking. Non-monetary benefits are those that are of no cost to the employer and do not provide for a transfer of money or services that save the employee any money. Recognition, thanks, and praise are non-monetary rewards, as would be reserving the closest parking space for the most productive employee of the month. Monetary benefits are fine, certainly, since it is hard to find employees who are completely unmotivated by money. But when monetary rewards are tied to some sort of competition, for example, a sales contest, this can make quite a dent in the camaraderie of the workforce. Also, some people will cheat, lie, and steal if there is enough to be gained from it. Of course, monetary benefits cost the company money, and this takes away from profits. There has to be enough gain, for instance, in increased sales or production, to make this worthwhile for the organization. The only disadvantage I can see to a non-monetary award is if it promotes too much competition within the workforce. But it is hard to see that anyone would lie, cheat, or steal to get a parking space closer to the office. And I can see no down side at all in recognizing a job well done, with a thank you and some praise.
I don't think a company can be run effectively without intrinsic and extrinsic rewards, both monetary and non-monetary. An effective manager knows which to use and when.