They sent you here? Guess what? For licensing questions we usually wave our hands and say that this is a technical forum, and licensing is legalese. Way over our heads.
I will need to admit that I have never heard of Standard-Server and Standard-Per Core. I know this distinction exists for Enterprise Edition, but I never heard about it for Standard.
Anyway, on https://learn.microsoft.com/en-us/sql/sql-server/editions-and-components-of-sql-server-2022?view=sql-server-ver17#scale-limits it says:
Limited to lesser of 4 sockets or 24 cores
And I take this to mean whichever pricing model you go for.
I checked the pricing page you linked to. The "Server" seems cheaper, but pay attention to the footnote:
Client access licenses (CALs) are required for every user or device accessing a server in the Server + CAL licensing model. See the product use rights for details.
So only if you need a very small amount of CALs, 12 or less, Server does not seem like a good deal. I should hasten to add that this is my understanding of that page after having spent less than five minutes on it.
Are there a different amount of cores that are supported between the Database Engine and Analysis Services?
According the page above, the Database Engine and Analysis Services have the same limits. It does not say that it would be the same 24 cores. But if you have a 48 core machine, you may have to play some affinity tricks to have them to use different cores.