It would be best to use the default setting of the group set which is Pass Through and to apply the mode changes on the layer rather than the Set. In this way, if you add more layers with different modes, Pass Through will blend any layer within the group as if there's no grouping,
I can't explain it in technical terms but changing the Set's mode to anything else will have a different, unexpected effect. It will blend the layers within the group first and the result is again blended with the layers below and outside the group using the blend mode selected for the group. Thus if you have say several layers in the group and set at different modes, the layer settings are cancelled out and will be blended in the mode that is set for that group.
So use Pass through - the Group set's default setting.
edit..... ohh Goooood lord.... less than 60 seconds apart with MrTom...... :banghead: :hi:
edit02...... I forgot to mention.... the effect you're getting with the group blend mode set to Linear Dodge with normal layer mode content is like painting the stripe directly on the base image (layer 1) with a brush set to Linear Dodge.
...you didn't ask how they worked, just why the same mode was giving you different results.
If you want to know how they work then I'm sure they can be explained to you, but the answer to your question is as simple as I've already pointed out....the blending mode is being applied twice, but only to one half of the image.
It has no effect at all as it's not part of the group. Even if you position the stripe next to the one on the left hand side ...... as my problem-reconstruct image shows....
The stripe on the extreme left is a duplicate of the stripe layer on right with layer set to LDodge. As you can see, both top layers have no effect to nor gains the attributes of the shape in the set (Set1) below them. Same thing if you position the layers below the Set.
BUT... if you drag the layer into the set, it's assigned layer mode is cancelled out and takes on the qualities assigned to the set's mode and will look exactly like its "room mate"... lol.
The small strip in the center is a brush stroke set to Linear Dodge applied directly on the layer image.
hmmmmm... I just noticed.... I should have used a soft edge brush for that small stroke so the burnt edges are much clearer to see.... oh well....
I think this will demystify it and explain better than I can....:banghead:.... lol