The best thing to do is learn the cooker and adapt to it. Do the dreaded biscuit or toast test. Despite some hating it, it is a good indicator of heat distribution across the grill surface. Additionally, or instead, line up 4-6 probes across the grate and run the smoker for a few hours changing the temps every hour or two and then reviewing the results. How much do they vary from left to right? If you are seeing significant differences in times for all cooks (of very similar sized/shaped comparisons), you're cooking at different temperatures despite what the controllers say on the two grills.
Every pellet grill is different, just like every model of any time of smoker is a little different. Ideally, there would be 3-4 probes in a pellet grill sitting a couple inches above the grate to and the controller would work on averages of them. However, they'd be in the way all the time and probably get frequently broken by the users, so grill companies use 1 probe usually either all the way to the hopper side or dead center in the very back to estimate the whole pit. The best solution is to use your Inkbird and put a grate probe a few inches away from your food, then adjust the pit accordingly to get the temp you want to cook at. Does it matter if you need to set the controller to 240 to get 225 by the food as long as you know? I'm also guessing that this discrepancy will stay pretty consistent over time and across temperatures unless you have large amounts of food in the cooker changing airflow. However, if your GMG was likely consistently hot, your expectations might take a while to reset. I'm also curious for learning purposes what raising a grate will improve? If you adjust the controller to get your desired grate level temp wouldn't the end result be the same? I've cooked via my Fireboard for years, I even adjust my MAK controller to get the Fireboard grate at the temp I want (though the MAK is usually very close unless it's really windy and/or cold, or I have a lot of food in it).
I'm also curious for more information regarding the comment about smoke output? I've reread your original post several times and can't find what the concern is, just the question of whether something would affect smoke? Are you feeling the Smokin Brothers imparts less or more smoke flavor than the GMG? If so, like others mentioned the newer controllers that hold tight temps often do have a milder smoke profile. If you're using different pellets, they could be affecting it too.