The score (or points) is the fundamental element in the Candy Crush saga. It is a statistic that is calculated during and after a level. The score will vary each time you complete a level, and each level has a passing score requirement.
However, many people tend to get the required score but do not complete the required tasks (depending on the type of level). Time and Movements levels are the only level types that only have a scoring requirement without completing other tasks, because scoring is the task in these levels.
The stars are obtained based on the score that the player has at the end of the level. One is the minimum and is required to pass the level, while three is the maximum.
In most jelly, ingredients, and candy order levels, completing the objectives directly gives the player the required score for a star. In a handful of them, completing the objectives directly gives the player the required score for three stars. There are some notable exceptions, like level 169 and pre-nerfed levels 608 and 623 (which is a copy of pre-nerfed level 608). However, getting two or three stars can be much more difficult at those same levels. This is quite troublesome in the mystery mission levels (on mobile devices) as the player is asked to get the 2-star score in addition to their task. This can be really problematic at levels like 297 and 463. At these levels, failure to meet the target score will cause the player to fail the level without the option to continue spending gold.
After the last jelly: 1 thousand pts
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For whatever reason, if you remove a gelatin or ingredient level without getting the required points for a star, your final score will rise to the one-star line and you will pass the level. This does not happen at candy order levels where you will fail after order fulfillment but don't have enough points even after sugar crushing. This also applies to mystery missions, except if your score is between the one-star line and the two-star line, it will not be increased now (it was increased to the two-star line in the past).
In the past, the score spike came after Sugar Crush. As of mobile v1.62, it occurs at the time of completing the objective (i.e. removing the last jelly square).
In recent releases (probably since v1.73), candy order levels also received this boost.