The meaning is the same, when spoken to a group of people. "Stand up" may be said to one person, while "all rise" may only be said to a group. However, you can tell one person, "Rise." The main difference between them is not in meaning, but in FEELING or MOOD. "Stand up" is very common, not very special. "All rise" has a formal mood. It is said when people are standing as a gesture of RESPECT (e.g., when a judge enters the court, when the bride enters the hall, etc.).

Stand up and all rise having the same meaning, but to the listeners, there is a great different. Using the proper diction is consider to be the good English for the English native speakers and scholars. As a native English speakers, we sense the meaning of the English words. We don't analyse the words by definition or restriction of the grammars. The feeling for the listerners on "stand up" is an order to do an act, you still deserve the right to refuse for performing such act, there are no restrictions to be used for statement. All rise is an a must act, you have to do it without any choice. For example: the rising sun. It is an necessity act to perform. In short, all rise is an necessity act to perform. The scholars massage the wording and dictions to be used for public speaking. You will hear more often at the court house.

Hello Flynn, Both words are asking a person or more ( stand up ) or a group of people (rise all) to assume a standing position after sitting or lying. In this case the difference in meaning (as Erik stated before) is in the casual changing of one's position to a more formal action related to ceremonies or special occasions."All rise" has also the connotation of showing special respect or admiration towards the person they are rising for, who tend to be superior in a way or the other ( age, position or at least as a main figure in a special occasion). "The children all rose when the headmaster came in." In fact they stood up but in high estimation of his person, thus using "rose". *Yet using "stand up" as a phrasal verb by adding the preposition "with" to stand up with makes the expression formal and related to wedding ceremonies in particular. It means to act as best man or maid of honor for (the groom or bride) at a wedding.