What is the similarities of the Labour and Product Market?

Answer 1

Classical and Neo-Classical economics kind of assume there's very little difference between those markets, except from the fact that labour supply is quite unelastic to wage, or that an increase in wage could actually decrease availability of labour on the market as workers might consider they need more leisure time.
The economics of information has also shown why wages were sticky, even in the absence of unions or state regulation, with insider-outsider models for example.

But many actually consider that the labour market actually doesn't exist, as a market.
Basic Keynesian economics show that supply and demand for labour are linked, as wage is a price, but also an income that fuels effective demand (on the product market).
Marxian approaches show that the relationship between employers and employees is more of a power struggle, as wages are the hidden form of exploitation is the capitalist system.
Sociology also shows the importance of networks in recruitment process, which has very little to do with a competitive market, even though the notion of social capital can be included, although imperfectly, in economic models.

In my personal experience, I would consider that using microeconomic tools to analyse an employment situation is way too limited and usually serves ideological positions.

Answer 2

It would be easier to list the differences because there's really only one. The supply of products is relatively easy to increase. There is no easy way to increase the availability of Labor.

Other than that they obey the same laws of supply and demand. Government meddling has established restrictions on the minimum price for wages, and additional taxes tacked onto the cost of labor, which artificially reduces the demand for labor. For products the equivalent would be to set minimum prices on goods.