Yeah, ain't nomenclature fun?! Reminds me of my time in college in my Zoology degree program. I hated Taxonomy (name this species... Bufo or Rana Whatever the Frack! [leapord frog]).
What I have seen this (based on other peoples definitions) called is an Extended Stress Test (push to a constant level for an extended period of time to find memory leaks, log file overflows, table/row lock contentions, etc.).
So, I am going to take from this that we are talking about an Extended Stress Test, or maybe more appropriately a "Soak Test" (I like that because you are trying to saturate the system under test).