In the SR5 rulebook, there are two sidebars on pages 279 and 280, respectively, dealing with the hermetic tradition and the shamanic tradition. I understand the difference between the two in regards to the differing attributes used for drain. But I don't get what it means for the two traditions to tie the 5 spell types to different "elements" or spirit types. For example, what does it mean, in game or in fluff, that a hermetic tradition has combat connected with fire and shamanic has combat connected to beasts? I get that shamans can't summon fire and her ethics can't summon beasts, but beyond that, what is the point of the connections?

Thanks,
Opti

I think this is a holdover from previous editions.

And it didn't mean jack squat then either.

It means two things, one RP and the other game mechanic.

The game mechanic is that you can only summon the five types of spirits listed in your tradition. So Hermetic magicians can't summon beast spirits.

The RP one is that the tasks you ask of your spirits should be in line with the type of spirit your tradition links it to. Meaning if you are a Hermetic magician you should only ask your Fire spirits to attack things and ask your Air spirit to use its conceal power.

Check under Reagents on page 316. It says in there that not all reagents are usable by all traditions, with a few examples. Once a magic supplement is released we'll likely see some details on what's what in the magical chemistry kit, but for now it seems to be more GM say so.

That's a little extreme. I wouldn't go further than saying that you should ask the fire spirit to attack things more often than any other type of spirit. Hermetics are all about the right tool for the right job, so if another spirit will perform better in this particular fight, pull it out. All else being equal, though, a hermetic wizard should call in the fire for fighting. Similar arguments would apply for most trads, really. There might be a few where it goes as far as saying calling a different type should be a rare and special occurrence, but for "only" I can't think of any, really.

As noted the Reagents section makes use of that chart.

I did say "should."

The spirit/spell type has to match on Aid Sorcery and Aid Study tasks.

It did and still does.
Aid Alchemy, Sorcery, and Study:As a service, the
spirit can add its Force as a dice pool bonus to your Alchemy, Spellcasting, Ritual Spellcasting (for spell rituals), and
Learning Tests if its type matches the spell’s category, as
listed under your tradition (p. 279).