@Buddy16, It’s important to understand your state homeschool laws. The MA [high school equivalency](http://www.ahem.info/HighSchoolDiplomas.html) does appear to be the HiSET. The TASC (Test of Secondary Completion, formerly the GED) is a federal exam, the HiSET is a MA test.
I’d take the HiSET and submit that to colleges. I think it looks better than the GED/TASC (even though the GED started as a college entrance exam for servicemen who enlisted in WWII before graduating from high school) because it’s so often now associated with high school drop outs.
NYS colleges will accept whatever the home state of the student takes as proof of substantial equivalency; you can check colleges in other states to see what they require, but I can’t imagine it’s different. As a NYS homeschooler, I’m required to follow NYS law, not the laws of other states, so when my son applied to college he sent his Letter of Substantial Equivalency to colleges in 6 or 7 different states and every one accepted it.