If the original Captain seems like a black and white version of Captain America, there’s a reason. When Steve Rogers got the boot by the government, he didn’t want to give up super heroism so he dropped the “America” and carried on as just the Captain. It was a strange idea and it didn’t last long. The Captain beat up his replacement and took his America back.
The most recent Captain of the Marvel universe is entirely unrelated to the first although I think they chose the name through a shared lack of imagination. The current Captain is none-too-bright, none-too-classy, none-too-sober and all schtick.
References: [marvel.fandom.com: Steve Rogers]
[wikipedia.org: Captain America]
[marvel.fandom.com: Captain (Nextwave)]
Metahuman Database 