From a professional point of view, this is how I define them:
Heavy-lift carrier: General cargo ship with cargo hold(s) and cargo handling gear (cranes, derricks) giving a single lift of minimum 100 tonnes SWL
Heavy-load carrier: Open, flat-deck cargo carrier without holds. Cargo handling is typically by flo-flo or ro-ro rather than lifting gear.
As I say, this is from my business standpoint and may not reflect how other data sources including those used by shipspotting.com define such vessels.
For the purposes of uploading and viewing photos on shipspotting.com, the generic category "Heavy-lift vessels" should be used. This category consists of both heavy-lift and heavy-load carriers. Indeed, if one refers to the 'heavy-lift' market in terms of the shipping industry, it refers to both types of ship so, before anyone asks, I don't believe there is a need to split the category into two.
"Strengthened for heavy cargo" is merely a classification notation. It means that a ship meets the classification society rules for having a deck or hold capable of handling cargoes of a certain weight which, for general cargo ships may mean project cargoes and for bulk carriers, iron ore.
Brgds
Phil