There are a number of terms, and it woudl not shock me if some equipment
used a term with a non-standard definition. The first thing you should
do is chase down what the words actually mean. Often heat index type
values are relative to 50% humidity. There's no reason to expect that
Heat Index and Feels Like have the same baseline treatment of humidity,
unless you read both definitions.
I have never seen a definition for "Feels Like". It seems to be an
acurite concept, basically heat index or wind chill, depending on
whether it is hot or cold, in some vague way. I would not be surprised
if there were a number of inconsistent definitions. I generally ignore
things like this, that aren't clearly traceable to a widely-agreed-on
definition backed up by the literature.
Weewx can use values from hardware or calculate. Read your weewx.conf
and look at the StdWXCalculate section, and read the docs about that.
https://en.wikipedia.org/wiki/Heat_index
There is also THSW, which I gather is popular in .au, but I am unclear
on it.