Yes the concept of LJ/SJ refers to the big end diameter. So both are LJ !
The crank on the right is a transitional crank, not particularly well mentioned in the english literature but used in the (if I remember this correctly) in the 56/57 american road rockets (road rockets were rarely seen in the UK) as they were snapping cranks with their 356 cams and 8:1 compression. The transitional crank is lovely and heavy and makes for a lovely smooth motor and has so much meat in it I can't imagine it flexing. It also has a different smaller sludge trap. The more common LJ crank on the left covered by all the literature came out in 58 and is much lighter.
I ran my race sidecar on a transitional crank for several years and it was extremely good, plenty of flywheel, nice for drifting. It was also very smooth. I've swapped this into my road bike and now racing on the later crank which does rev slightly quicker having much less weight. It should be noted the heavier cranks weight is central so they are one stiff sucker, but I suspect the later type were cheaper to make.
In practice use whichever is less worn and clean the sludge trap very thoroughly
