The short answer is no .... but in some circumstances yes...
1) Each seed is created when a flowers embryo is fertilised by a grain of pollen.. If the plant is perfectly homozygous and self fertilizes, then 'yes' the genetic code in each seed should be close (there's always mother nature interfering lol) if not perfectly the same.
2) If the father plant and mother plant are both homozygous and of the same geno then the same theory should apply..
3) If the father plant is a different variety to the mother but both are homozygous, then once again the seeds should be the same, that being said ongoing generations will not be due to recessive traits. This is caused by each plant giving 50% of the Geno and through breeding further generations having recessives come to the surface.
4) If one or both parents are Heterozygous then when pollen hits embryo there is a 50% chance for one of each pair of genes to go to the final seed. So in this case you could expect a Yellow pod seed to be next to a red pod seed in the same fruit etc. as each pollen attaches to an embryo there is a DNA dice roll at that that conception moment, the only reason it appears that stable plants don't dice roll is all the numbers on the dice have been made the same an example
- Parent A) RED / yellow ( or R/y) Parent B) yellow / RED or (y/R)
There is be a 25% chance that the seed could be a Red with a no recessive's ( or R/R ) a 50% chance its Red with recessive Yellow ( or R/y and y/R ) and 25% its Yellow with no recessive ( or y/y ) check out Mendel's law for more info.. That ALL being said, In this circumstance each seed COULD and will be different, any exact matches will be coincidental.
5) There is also the possibility that two completely different Father parents or more.. could fertilise a flower.. And therefor mix up the DNA even more.. ( This can be accomplished by mixing up pollen from several plants and manually pollinating a flower with it )
Mother plant
Plant A - Mother Plant
Father plants - Pollen mixed
Plant B - Pollen mixed
Plant C - Pollen mixed
Plant D - Pollen mixed
End result of lets say 7 seeds in pod.
AB - AC - AC -AD - AB - AC - AB could be theoretical possibilities. ( This is sound science and I plan on embarking down this path soon for fun )
6) From there you have even more possibilities
If all 4 parents were Heterozygous then you could have a HUGE range of possibilities for the seeds.. !!!!
--- There is a WHOLE other topic about pepper stabilisation relating to this ---
But to answer your question, each seed is its own unique being that CAN contain varying genes.. even Identical ones are only identical through chance or purity of strain .. not by default.
*** This is the reason behind people breeding homozygous or stable varieties.. Imagine breeding a pepper with a green parent and a yellow parent with another pod with a red parent and brown parent and wanting to refine the colour to green in your future pods.. You have a whole lot of gene clutter to get through to stabilise those pods. Much easier to get a green / green pod and mix it with a YELLOW / YELLOW and look for that 25% chance of green.
*** Sorry I just read your post again and realised I started on dominant / recessive info that you already know about.. But in essence its relevant in some ways to each pod containing varying genetic codes in each seed...