Two firms can sell an almost identical product and still behave in completely different ways, purely because of how much competition each one actually faces. Economists organise this into a spectrum of market structures — running from perfect competition, where many firms sell an identical product and none has any power to influence the price, through monopolistic competition and oligopoly, to monopoly, where a single firm faces no direct competitor at all. A firm's position on that spectrum, more than almost any other factor, determines how it prices its product and how much output it actually produces.
Perfect competition leaves a firm no pricing power at all
In a perfectly competitive market — a stylised model rarely fully realised in practice, but a useful reference point — many firms sell an identical, undifferentiated product, and any single firm is too small, relative to the whole market, to affect the market price by changing how much it produces. A perfectly competitive firm is a "price taker": it has to sell at whatever the market price happens to be, since charging even slightly more would send buyers to a competitor selling the identical product for less. Its only real decision is how much to produce at that fixed price, not what price to charge, because it has no power over price at all.
Monopoly gives a firm full pricing power, and a different set of constraints
A monopolist, at the opposite end of the spectrum, faces no direct competitor and therefore does have genuine power over price — but that power isn't unlimited, because the monopolist still faces the market's overall demand curve, and raising price still reduces the quantity buyers are willing to purchase. A monopolist's actual decision problem is choosing the price-and-quantity combination that maximises profit given that demand curve, a genuinely different optimisation problem from a competitive firm's, which simply produces up to the point where its cost of producing one more unit matches the fixed market price. Oligopoly and monopolistic competition, sitting between these two extremes, introduce further complications neither pure model captures cleanly — oligopolists have to account for how rivals will respond to their own pricing and output decisions, since there are few enough competitors that each firm's choices meaningfully affect the others, a strategic dimension that neither perfect competition nor pure monopoly needs to consider at all.
What we're still unsure about
The theoretical models describing behaviour under perfect competition, monopoly, oligopoly, and monopolistic competition are well established and rigorously derived within economics, and are useful reference points for analysing real markets. What's harder to settle with precision is classifying any specific real-world market cleanly into one of these categories, since real industries rarely match the idealised assumptions of any single model exactly — most real markets sit somewhere in a messier middle ground, with elements of product differentiation, limited but real competitive pressure, and strategic interaction all present simultaneously, which is why applied industrial economics spends considerable effort on empirical methods for measuring market power and competition in specific real industries, rather than relying on the clean theoretical categories alone.
This sits inside Market Structures (Perfect Competition, Monopoly, Oligopoly), one of eight topics in Microeconomics, one of five domains in Economics, one of seventeen subjects the app can quiz you on.