The plugs you purchased were probably the small 5/8ths plugs that have tapered seats. The plugs you took out of the engine are probably the larger plugs which require a 13/16 inch socket and have flat seats with a washer.
If the engine is from the sixties and early seventies, it has a pre-smog head and requires the larger plugs. You should need AC Delco Plug R44XL. Also, Champion 4N14Y plugs will work.
Spark plugs of various brands can be used in different makes of engines. I use AC Delco in my GM engines. Some people prefer Champion spark plugs in Mopar engines, but they will also work in others. Aside from the swapping of different brands of spark plugs, no you cannot use Dodge parts on/in your Chevy engine.