The LA designation stands for "Light A" engine. The A engines were the 318's, 360's and I believe 340's from the early Mopar days. The 340 was discontinued by 1970, and I can't recall if any were ever built as an LA option.
The light designation is a reduction in weight by thinning the block castings. I think they saved something like 53lbs off the engine block by casting thinner. This lead to obvious weight savings, reduced raw material manufacturing costs, better heat dissipation and greater fuel economy, at the expense of reducing the number of times the block could be safely machined and the bore enlarged.
A magnum engine is a re-engineered LA block with Magnum heads. Better intake port flow, combustion chamber design, as well as pedestal mount rockers with a 1.6 ratio and more secure valve covers are the big differences between the LA and Magnum heads. Magnum heads can be drilled to bolt on to certain LA engines for a nice performance gain.
The engines were sightly changed with direct-oil thru pushrods, a vertical mounted intake manifold, hydraulic roller lifters and camshaft, electric fuel pump instead of camshaft driven, multi-port computer controlled fuel injection, and a few other goodies I can't recall right now. Some of the very late LA blocks may have been hydraulic roller, I don't know when the exact switch was. All LA's were either carbed, or very late models were TB injection engines.