The NYT reported that the Trump administration is considering replacing the tariffs it imposed on aluminum and steel imports from Mexico and Canada with a system of quotas. There is an important economic dimension to such a shift that was left out of the piece.
If the US imposes a tariff on an import then it is effectively imposing a tax on US consumers. The government gets to keep the revenue. For example, if steel is imported at a price of $700 a ton and we impose a 10 percent tariff, then the price of steel to consumers rises to $770 a ton with the government getting $70 for each ton that is imported. (For simplicity, this assumes that the tariff does not affect the price of the steel. In reality, it will fall somewhat in response to the tariff.)
If we impose a quota that leaves imports at the same volume as with the tariff, then the price of steel will rise to the same level, or $770 a ton. However, in this case, while steel consumers are paying the same higher price, the money is not going to the government. The extra $70 a ton is going to the steel producers.
While restricting the volume of their sales, the US government is allowing foreign producers to get more profit on each ton of steel they expect to sell to the United States. For this reason, quotas are generally much more acceptable to our trading partners than tariffs.
When the United States imposed quotas on Japanese car exports in the 1980s (actually "voluntary export restraints") Japanese manufacturers used it as an opportunity to move into more upscale cars. Originally, Toyota and Honda made large inroads into the US market by competing in the bottom segment of the market. Since they were limited in the quantities they could sell, they could make more money per car competing in the higher end of the market.