The only heal type that is affected by the regen rate is the heal over time shield heals since their bonus to regen stacks over the base shield regen amount.
I would have to do some testing, but I'm not sure this is accurate. HoTs (such as TSS or RSF) as far as I'm aware are considered heals, not regeneration (they show up in your combat log and flash as on-screen numbers, passive regeneration does not).
I could be mistaken but I always assumed the shield modifier influences shield capacity (health points). Specifically, 0.9 shield modifier number gets you 90% of the shield maximum capacity, 1.1 gets you 10% more over the shield maximum capacity. The bigger your shield capacity is, the better simply because you don't want your shield to regenerate so fast that some of those heals are wasted.
Shield regeneration is how fast you can refill your shield's facings. Regen passives add up or multiple if %. These regeneration rates are usually affected by shield power levels, how many points you've spec'ed in starship skill abilities (such as emitters) and boff abilities (i.e emergency power to shields etc)...
**~Reality under scrutiny~**
Fed Fleet: Operation Omega Task Force | KDF Fleet: KHG Klingon Honor Guard