This question is too broad as it's asked. Obviously, you should talk to you HR or the insurer, don't just assume things. But, as I don't think this person is coming back to give details but the system bumped this question to the top I'll go over the catching points for anyone else who may stumble here in the future.
It's very very very plausible that plan A has a deductible of $X and the $4,000 Coinsurance maximum accrues separately after the deductible is met.
This could occur under two scenarios:
There aren't many grandfathered plans out in the wild anymore but there are some and plan A might be one. If so throw away almost everything you read about "what's allowed" because there's a completely different rule book and deductibles and copays might not apply to "maximums."
If the plan is not grandfathered some carriers still present plans this way; with deductible and coinsurance indicated separately. The deductible plus the coinsurance maximum must still be below the maximum allowed out of pocket maximum allowed by the ACA, which for 2019 is $7,900.
With Plan B, there might be a deductible but it's explicitly indicating that your out of pocket maximum exposure is $4,100.
Without a pretty substantial amount of additional information it's not possible to say one way or another. So:
Under Plan 70/30 am I still on the hook for fees above $4000?
Maybe. If the plan is non-grandfathered, you could be on the hook up to $7,900 for 2019, if grandfathered, potentially higher.
And under Plan 80/20 I am NOT liable for ANYTHING above $4100?
Probably not. Though, ANYTHING refers to dollars spent on covered services. As an example, if your insurer approves 10 physical therapy visits but you go to 15 physical therapy visits, it doesn't matter that physical therapy is a covered benefit the additional 5 visits are not covered.