The logic that differentiates them is similar to "lie" and "lay." Lying is the act of the entity in a resting position, much like how you "lie on the bed" before you go to sleep. Laying is the act of being put down literally, like the way you "lay" a book down on the table.
Please note that "lie" can be used to refer where an entity is positioned or how it remains. Examples: (1) "Todai lies in the heart of Tokyo;" (2) "The Jewish Museum of Belgium now lies in ruin." Another use is that, albeit it's quite obvious, is being dishonest or untruthful ("You lied to me! You told me there would be cookies!).
Rising is the entity "rising" (moving up from a lower position) on its own while raising is the entity "being raised up," usually by an external force. Imagine that "rise" is like a cake or bread in the oven as it cooks ("the cake/bread rising") or students rising from their seats to greet their teacher as he/she enters the room. On the other hand, imagine that "raise" is like a mother/father picks up hi/her baby from the crib (the ACT of elevating or lifting the object, or in this case, baby), or a market-goer raising his/her basket of apples in the busy market to avoid dropping the fruits whilst trudging through the bustling crowd.
Note that "rise" can be used as a metaphor to refer to individuals gaining popularity, used like "a rising model." Another use is when someone recovers from defeat and regains his/her glory, like "rising from the ashes of defeat" (imagine the legend of the phoenix). On another hand, "raise" is also often used to refer to the upbringing a child, or "the way the child was raised."
(In case you wonder some day, a formal word for "rise" is "arise.")
I hope I helped you understand the differences. If you need more analogies to further understand please do let me know.