What snippets of info are you basing this on? The official curb weight difference between SR and LR is 120kg. Looks like extra modules to me. Say, 5 modules of ~10.5kWh for the SR, 8 modules for the LR. Possiby one with fewer cells, or simply some extra capacity to play with on the LR pack which is so well paid (~$400/kWh for the upgrade alone, 3-4x cost).At the official rate of 237 Wh/mi (is this for the T3?) for the base model 3 I get a battery pack of 96x43 cells, each cell 3.4 Ah (i.e. a Panasonic 18650 or a 'low-capacity' 2170). This gives a storage capacity of 51 kWh, and a capacity of 54 kWh when 6% top and bottom buffers are included. It is interesting to note that the TS100D is a 96x86 architecture, i.e. exactly double the number of cells of the T3SR.
The T3LR comes out at 96x43 cells for a storage capacity of 73 kWh and 78 kWh respectively (average is about 75 kWh). Each cell is 4.9 Ah, which is probably what a 'standard capacity' 2170 is.
In the longer term, we should see the range of the T3SR creeping up to 230 and 250 miles at the same price, because it does not cost much for Tesla to increase their range and there is ample room for the increase. The T3LR will also increase its range, but because it is out of room, it will increase much slower. Most likely, Tesla will use the upgrade room for the T3SR and move it to let's say 260 miles, while offering a "software crippled version" at 215 miles at the same price, and asking for a premium for the 260 mile version to uncripple the vehicle.
SR could also be 6 modules each with a few cells less than fits, LR 8 very full modules of ~9.5kWh each.