Purslane on right, spurge on left. Spurge stays small and delicate, purslane continues to grow leaves thick and about 2-3 cm, stem thickens to about 1cm and about 24cm long. Purslane is also more sedum like in appearance. Hope this helps. Spurge also leaks white "milk" when cut. This can be an irritation to your skin. It is to me so I wear gloves.
The spurge is a euphorbia, which are toxic. Some other euphorbias are another weed called toothed spurge (I've seen some on here & I also had some growing in a pot somehow), crown of thorns (gorgeous plants), & pencil cactus. There's like thousands more. The milky substance has been known to cause rashes, blindness, & excruciating pain in the eyes. Always use caution when handling any euphorbias.
You are right. The source I read says there are 500 varieties of euphoria. We sold a couple varieties at the nursery I worked at a few years ago. I think they all succeed this milky substance. One really needs care when handling these plants. Some are quite beautiful. Even using gloves I still get a rash from them.