Not sure at all since I am not very familiar with these old concepts.
But I think what you call LLM (not a very common concept it seems) are algorithms that solve linearly separable data classification. SVM are algorithms that look for an hyperplane that maximize the margin with data and thus can be considered LLM. Quick reminder how a SVM solves a linearly separable problem :
We escape LLM's grasp when trying to solve a nonlinear classification problem, as represented on the left of the following picture.
SVM can still solve these type of classification with the kernel trick, that applies a non-linear function to turn the classification into a linear problem.
Hope this can help your understanding of the difference, all images are from Wikipedia. My apologies for not knowing how to resize these images :(