It's the same thing really. If you turn up in Flight Connections with a missed flight the agents will immediately see that it wasn't a connection, and while you can do your best to negotiate a better outcome, formally BA will just say, correctly if unhelpfully, "separate contracts". Generally you can work out if this is going to happen before take-off from the previous sector, since with a given take-off time, plus block time, you can work out if you are going to hit conformance or not. At which point you call or look manically at any Avios options for later that day. But if booking different tickets you do need to think that through very carefully in terms of timings, such as looking at twice Standard Deviation on average delays and what-not.