The US deliberately set out to create second-strike weapons — weapons that would survive a first strike attack. In terms of what they looked liked technically, these were weapons that were either heavily shielded (like ICBM silos that could withstand near misses), or easily hidden (submarines are the obvious candidates here, but they also discussed alternative options like putting mobile, long-range ICBMs onto trains and moving them around all the time).

They also ended up with weapons that were extremely vulnerable, and were thus only useful as first-strike weapons. So the Jupiter missiles they put in Turkey in the early 1960s, for example, were above-ground, combustible, next to the Soviet border, took a long time to fuel, and would be just completely sitting ducks if the Soviets decided to attack first (they could easily be destroyed by even non-nuclear means). So the only possible use for such a weapon would be to launch a first strike, because they utterly lacked the ability to survive anything else.

Other than these kinds of approaches, there wasn't a lot of differentiation between the two. There were general technical/strategic desires — to have a weapon that was survivable, to be able to rapidly wage a decapitating attack if it was felt that it was the right call to make at the time — but they didn't generally say, "oh, this weapon is part of our first-strike capability." They had different roles for the weapon systems but they were generally more fine-grained than first or second strike.