Payload is vertical weight in the bed.
Tongue weight is, of course, vertical weight on the tongue.
Towing capacity is horizontal pull/drag while moving forward.
Combined weights, all told, should not exceed gross vehicle weight; tongue weight, payload, vehicle curb weight, people. Tongue weight does impact payload. Payload does not impact tongue weight.
Everything above is all a matter of degrees.
For easy numbers - Let's say you have a 2000lb total payload limit, currently have 1500 lbs in your bed and you add 500 lbs tongue weight on your hitch, you're now at max payload of 2000 (or thereabouts, given weight over axle, weight behind axle, levering, etc. )
Now let's say you have 2000 lb total payload limit, currently have 500 lbs on your hitch tongue, and you load your bike in the back of the truck (~600 lbs). You have NOT added to your tongue weight, so you're still good on the trailer, but you've taken 600 lbs away from your provisional cargo, and currently sit at ~1100lbs in payload.
With a 10k towing weight, putting your bike in the trailer over the axle *could* conceivably not increase your tongue weight much at all, thus not impacting your payload weight, and would only impact your towing capacity; assuming your trailer is also set up to haul bikes.
All of this is estimated, of course, and you should always strive to remain at least 30% under your limits for reserve.