What is the term for varying types of selection, and why are most apps either one/the other with no setting

This might be asked before, but I'm trying to create a feature for my design app that supports both methods of selection in this way. One mode should select all items that the bounding box even touches a little bit of the item in question, it selects it. Example here (bounding box is black, green is selected, red is omitted):

The other type of selection is more strict, and only selects ones that are completely within the box.

Additionally, most apps that I found are usually one or the other (either that or I haven't found the setting because I don't know how to look for it). For instance, Illustrator defaults as the first option, but some apps like Solidworks in 2D mode default as the 2nd option. Despite this being a really simple feature, it can severely improve or otherwise hamper some simple tasks; like if the objects are really close to one another, the 2nd option is better for precision. Apologies if this is actually a duplicate, I have no idea how to explain this to Google. Thanks y'all!