According to this question forage points are limited per area. If there are 6 items on the ground is it impossible for a worm space or a bubbly water spot to spawn? Or are they considered independent of "foraging" spots and can spawn anywhere at any time?
After taking a look at the source (as of V1.07) it seems that splash points do not count towards the forage points. Only a single splash point can exist in a location and they will never spawn on your farm. If a splash point is not present at a location it will attempt to spawn one by testing a random point on the map at about a 50% rate every time the game updates for the 10 minute interval. If a splash point exists it will have a 10% chance of being removed during the tick. Additionally it looks like if you are on the map that a splash point is spawning you should hear a water slosh sound play.
The worm spots also do not add to the forage points. There is no hard limit on how many worm spots can spawn in a location. At the beginning of the day each map location is given several chances to spawn worm spots (this is done the same method which adds forage spots). The game will keep trying to add worm spots until it fails a check, with the likelihood of passing the check becoming less each round...during the winter ~10% chance is added at the end of each round with the result being the spots happening more frequently during that season. After passing the initial check a random spot is chosen and tested to see if it is suitable, a spot will only be added if it passes the tests.