Index providers commonly avoid the dollar problem by not using dollars. Rather than fixing a boundary, a provider can define a size segment as a share of a market's total value. MSCI's Emerging Markets index, for example, "captures large and mid cap representation" across the countries it covers and reaches "approximately 85% of the free float-adjusted market capitalization in each country," which means the companies below that line are what the segment excludes. Defined that way, the boundary is different in every country, it moves as prices move, and it never needs revising as markets grow. The practical consequence is that a fund's own documents, not a dollar figure, determine what it means by small.
The consequence of a floating convention is that the same company can be labeled two ways at once, by two sources both using the ordinary meaning of the words. That is not sloppiness. It is what "no fixed cutoff points" means in practice, and it is a reason to read a fund's index rather than its name.
Where the additional risk comes from, stated structurally rather than statistically. Smaller companies are typically less diversified across products, customers and regions, so a single lost contract or a single regulatory decision can matter to the whole business. They generally have narrower access to capital, which makes a downturn harder to fund through. Their shares trade less, so the gap between the price at which shares can be bought and the price at which they can be sold tends to be wider, which is a real cost paid twice on every round trip. And fewer analysts follow them, which is simultaneously the argument for the category, since less-examined companies are more likely to be mispriced, and the reason the information a buyer is working from is thinner.
Smaller still. FINRA notes that "you might also hear about micro-cap companies, which are even smaller than other small-cap companies," and elsewhere describes microcap securities as sometimes being referred to as penny stocks. The terms overlap loosely in ordinary use, and the reporting and liquidity concerns at that end of the market are their own subject.
What a small-cap fund is actually doing to a portfolio. A broad cap-weighted fund covering the whole market already holds small companies, at the weight the market assigns them, which is a small weight precisely because they are small. Adding a dedicated small-cap fund does not add a missing exposure. It deliberately holds more of that exposure than the market does, which is an active decision and requires a reason beyond wanting to be diversified. Whether small companies compensate holders for their extra risk over long periods is a contested question in the research literature, and no claim about it belongs on either side of that decision.