I have put an app in the Exchange called URL Formuals for Dummies. It helps explain these URL formuals.
I will brerak down your code
URLRoot() // that means mycompany.quickbase.com
& "db/" // you will see that in almost every Quick Base URL
& [_DBID_ID] // this identifies which table in your app
& "? //this tells the internet that parameters follow and just deliver the parameters to the website (ie Quick Base)
a=API_GenAddRecordForm // this is an API to put up and Add Record form.
&dfid=10 /this say to use firm ID# 10 in place of the default form.
&_fid_15=" & URLEncode ([Record ID#]) // this says to preload into field ID the value of Record ID# from the Parent Record that you launched off if.
& "&z=" & Rurl() // that means that upon save to return to where you launches from instead of displaying the newly created record.
so yes, you need to specify which API you are calling when you call an API.