Difference between aggregation and operator

For querying data in MongoDB you can use the find method or the aggregate method. There are operators which you can use with these methods.

These query operators are used with the find method. Some of these can also used with the $match stage of the aggregate method (details later in the post).

These aggregation pipeline operators are used within the aggregate's stages. Some of these can also be used with the find method (details later in the post).

You will notice that, there are common operator names; for example, $eq, $gte, $or, $type, $size, etc. But, their usage and / or functionality can be different. The $eq operator has same function but different usage syntax and the $typeoperator has different functionality (and usage syntax).

And, some of these operators can be used with both the methods.

Some Usage Scenarios:

Lets consider a users collection and some queries:

{ "_id" : 1, "age" : 21, "firstname" : "John" }
{ "_id" : 2, "age" : 18, "firstname" : "John" }
{ "_id" : 3, "age" : "39", "firstname" : "Johnson" }

The query:

db.users.find( { firstname: { $eq: "John"}, age: { $gt: 20 } } )

This query's filter is same as { firstname: "John"}, age: { $gt: 20 } }. This uses the query operators $eq and $gt. The same query can be written in the aggregate method's $match stage:

db.users.aggregate([
  { $match: { firstname: "John", age: { $gt: 20 } } },
])

The operators used in this case are the same query operators. The query comparison operators can be used with the aggregate method's $match and $lookup stages.

db.users.aggregate([
  { $project: { ageGreaterThan20: { $gt: [ "$age", 20 ] } } },
])

This is the usage of aggregation comparison operator $gt. Note this is used within the aggregation query, but within the $project stage.

As you had used the query operators in the aggregation query, you can also use the aggregation operators within the find method. But, this must be used with the "special" $expr operator. For example:

db.users.find( { $expr: { $gt: [ "$age", 20 ] } } )

The advantage of the $expr is that - there are number of aggregation operators which can be used within the find queries. For example, using the $strLenCP:

db.users.find( { $expr: { $gt: [ { $strLenCP: "$firstname" }, 4 ] } } )

You can also use the $expr within the aggregation, within the $match or $lookup stages:

db.users.aggregate([
  { $match: { $expr: { $gt: [ "$age", 20 ] } } },
])

Finally:

I have been reading up on some mongodb documentation and ran across some confusing terminology, namely how to differentiate when a symbol will be used as an aggregate function or as an operator. ... but is there some rule/guideline so I can know what it will do beforehand?

Reading helps, practicing helps better and experience helps the best. You use a specific operator in a specific scenario or use case. To achieve some functionality you use an appropriate method and operator(s).

Reference: Operators

As per my understanding, I'm pointing out few things :

Difference between aggregation and operator

You'll have certain basic functions for crud operations like .find() or .insert() or .delete() or .update() on MongoDB (There are few others like .count(), .distinct() but those are primary)

Versus

aggregation is a whole framework heavily used for complex reads, only two stages in aggregation is capable of writes $out and $merge.

Operators :

There are different types of operators :

Query and Projection Operators : These operators are crucial and are used to filter docs and to transform fields of docs in the response, Usually used in filter and project part of .find(filter, project) or .update(filter, update, project/options) etc.. These are also used in $match stage of aggregation pipeline ($match is similar to filter in .find()). Ex. :- $and, $or, $in, $or & more.

Update Operators : By name, these operators help to update documents in the collection. Usually used in update part of .update() or .findOneAndUpdate() etc.. Ex. :- $set, $unset, $inc & more.

Aggregation :

When it comes to aggregation they call it aggregation framework, definitely for a reason as you can do a lot of things with data using aggregation.

Aggregation has aggregation pipeline , which has syntax .aggregate([]). pipeline is an array with stages. Each stage in aggregation does certain operation on data flowing through them. Ex. :- $match, $project, $group etc..

As we know each document is independent on it's own, most of aggregation stages operate independently on each doc flowing through them.

Aggregation pipeline Operators :

These operators are generally used to achieve what you're looking for, certain operators can't be used in conjunction with other operators or in a stage. Let's say in $match stage you would mostly use Query operators but not Aggregation operators as aggregation operators can't directly be used in $match in contrast with $project or $addFields stages.

Example with Stages & Operators :

Let's say you got to make Smoothie :

1. Out of a bunch of groceries you would filter needed fruits(docs in fruits collection) by matching with what you wanted to blend using $match stage ($and to match fruits/veggies, $lt to filter only fruits that hasn't expired and $size to limit no.of fruits needed).
2. You would peel off skin or chop into pieces to keep just keep useful parts of fruits(docs) using $project.
3. You would group all of the fruits into a blender using $group & add ingredients like cream & sugar using $addFields - You're too cautious about sugar quantity so you'll use operators like $size to check size and $multiply no.of nutrients based on conditions ($cond) you would $divide both sugar/nutrients to count nutrition value.
4. You'll iterate on adding ice pieces again and again using $map, $filter to remove un crushed ice pieces.
5. uhh, you always forget to add veggies (A different collection needs to be merged) based on fruits that already got blended you use $lookup to lookup for matching veggies(docs) & either blend in again with group or just put it on top.
6. Finally either you drink it from blender (just return the docs no more stages) or take into glass using $out or $merge stage (Remember as I said, only two stages that can write to a collection).

Off course every stage is Optional - You can eat fruits as is instead of blending (get all docs and all their fields) but you know what you wouldn't do that (for many reasons like performance, unnecessary data flowing through network) unless it's pre-prepared product (like a small configuration collection which has limited data with few docs & every doc is need & can be easily retrieved in one DB call).

Note :

Usually you can't use aggregation operators in filter part i.e; .find(filter) or in '$match' stage unless you use $expr.

Starting MongoDB v4.2 you can run aggregation pipeline in update-with-an-aggregation-pipeline where you can take advantage of aggregation stages/operators in update part.

While you search MongoDB's documentation often you would find the same operator in multiple places, Let's say if you search for $size you would find multiple references one is Query operator or as Projection operator or as aggregation operator - So depends on need/where you wanted to use you can refer their documentation for usage cause though name seems to be similar or does almost same but functionality may differ & syntax also differs.

You can always MongoDB for free at MongoDB University.