Ford,
I think that you might be referring to an inverter system that also has an integral charger, versus a sole-function inverter. (As far as receiving input DC power from a source, I do not think that the type of battery has any effect upon what type of inverter.)
Lifeline is a brand of AGM batteries (Absorbed Glass Mat) which use a different charging algorithm than flooded batteries.
My last knowledge of inverters was more than 25 years ago, and back then Xantrex (formerly "Trace" inverters; http://www.midnitesolar.com/pages/frontPage/nwHistory/history.php) had a good reputation. My
knowledge is stale so I need to make that decision also: what brand of inverter, and Magnum, from what I have read so far, gets good reviews.