Discerning a Spell

Sometimes, characters wish to try to discern what spell is being cast or if a spell is being cast at all. In the most common case, characters are trying to do this while in combat. However, this task isn’t as easy as it sounds - especially in an intense and rapidly developing situation such as combat. While under pressure, it is very easy to miss things that would otherwise be very obvious or easily understood. Many misunderstandings and mistakes happen when a reaction to an event is required but the time to make such a reaction is incredibly short.
However, in order to give some kind of concrete method of discerning these things and making things fair, the following mechanics will be used:

Is a Spell Being Cast?

Determining if a spell is being cast will always be treated as a Passive Arcana check. For example, a Wizard with +5 Arcana will have a 15 Passive Arcana.
The DC for this check is equal to 20 minus the spell’s casting time (0 {Reaction}, 2 {Bonus Action}, 5 {Action}, or 10 {1 Minute or longer}), and minus how many component types the spell requires (1 to 3 {Verbal, Somatic, and Material}). However, if the spell is cast with the Subtle Spell metamagic option, the DC is either increased by 10 or is impossible to discern (based on some conditions explained below).
Simplified Formula:

DC = 20 - (Target Casting Time) - (Required Components)

This formula represents how it’s easier to know if a spell is being cast because certain spells are more complex, and using a Passive Check takes into account those who have strong knowledge in the field of magic. However, this has not yet taken into consideration 3 other important factors: Ritual Casting, Subtle Spell, and Truesight.
If you are casting a spell as a ritual, anyone with even cursory knowledge of magic will know you are using magic in some way. Casting a spell as a ritual will require creative solutions to conceal if you wish to hide it from prying eyes.
If you are a Sorcerer (or have the Metamagic Adept feat) and have the Subtle Spell metamagic option, your subtly cast spells will be impossible to discern as long as the spell does not require any material components and/or you have the element of surprise. If you meet neither of those conditions, it is still possible for someone to determine you are in the process of casting a spell, but it will be much more difficult than normal (+10 DC). Regardless, the Subtle Spell metamagic option removes the Verbal and Somatic components of spellcasting, therefore making 'Required Components' equal to 0 so long as no material component is required.
Lastly, if you have Truesight, you are capable of seeing faint ripples of the Weave within your Truesight range which makes it easier to know if a spell is being cast (-5 DC) by anyone within that same range. This also allows you to discern if spells are being cast even if the caster uses Subtle Spell. However, this does not completely negate the difficulty that such Metamagic imposes. Ripples in the Weave can happen randomly, and not every ripple originates from a spellcaster.
Final Formula, assuming discernment is possible:

DC = 20 - (Time) - (Components) + (Subtle?) - (Truesight?)

This DC has a minimum of 2 and a maximum of 30, excluding situations deemed impossible due to Subtle Spell. Discerning if a spell is being cast does not require any type of action, but may only be performed or “checked” against one target every “round” (6 seconds).

What Spell is it?

Assuming you know that a spell is being cast, now you might want to know which specific spell is being cast. There are many potential reasons why you might want to know this information, but identifying a specific spell is more difficult than simply knowing if magic is being performed at all.
Instead of a Passive check, this will be an Active check (meaning you will roll a d20) which follows similar rules to determining if a spell is being cast in the first place. The type of check you perform is based on the type of magic your target is using.
The DC for this check is equal to 25 plus half the base level of the spell (rounded up; Cantrips equal 0), minus your knowledge level with magic (the highest level spell slot available to you), minus the number of components (5 [V,S,M], 3 [any two], 1 [any one], 0 [Subtle Spell with no Material]), and minus its Casting Time (0 [Reaction], 2 [Bonus Action], 5 [Action], 10 [1 Minute or longer]).
This formula represents the rarity and complexity of powerful spells which makes them more difficult to identify, how certain spells have signature components that make them easier to identify, the difficulty of identifying fast spells and the ease of identifying slow spells, how obscuring such components will drastically change the difficulty factor, and rewards those who have the proper knowledge with an easier time identifying the spell overall.
Full Formula:

DC = 25 + (RoundUp{Base Level/2}) - (Knowledge) - (Components) - (Time)

This DC has a minimum of 1 and a maximum of 30. Attempting to determine the specific spell being cast does not require any kind of action, but may only be performed once per round (6 seconds).
Unless you have at least one of the following, you have disadvantage on your check to determine what spell is being cast:

• Spellcasting trait
• Pact Magic trait
• Proficiency in Arcana
• Mage Slayer feat