They do similar tasks, but they are almost completely different because comparators output digital signals. In that case, I am confused as to why their schematic symbol is almost entirely the same. Is it implying something else that I am not realizing?
They are not completely different. They are much more similar than you think.
Technically, a comparator is just an op-amp optimized to operate in the saturation region (have the output saturate since it is always either LO or HI, but be able to leave saturation quickly for fast switching). Being linear in the linear region is not a design priority.
An op-amp is a comparator optimized to operate in the linear region (to be very linear in the linear region where it will spend all its time due to negative feedback). An op-amp used as a comparator will be slower since it is slow to get out of saturation.
Most opamps also have frequency compensation so that they can be easily used with negative feedback. Comparators have no need for such a thing.
Those are the big ones but op-amps also tend to place higher priority on things like noise, offset, and input bias currents than comparators. All that good analog stuff.
A comparator is often close to being a linear amplifier that is optimised to achieve rapid switching around the point where the voltage difference between two inputs are very close to zero.
A comparator MAY include hysteresis which makes it less linear in action, but this is not an essential component.
If you look at the block diagrams of the very old (and so simple) LM324 opamp and LM339 comparator you'll see that they are very very similar to each other internally.
LM324 opamp at left. LM339 comparator at right.
The opamp (operational amplifier) has added linear output stages - but shares the same longtailed-pair front end with the comparator.
An output stage of the users choice could employ the comparator as an amplifier - with potentially superior characteristics to the "linear" device.
The comparator is a mixed device with analog input and digital output; so it can be considered as a 1-bit analog-to-digital converter (just as one flip-flop can be considered as a 1-bit register).
Usually, the comparator output is implemented as an open collector stage. This allows to make it compatible with various circuit inputs and to connect multiple outputs in "wired OR".
A common practice is comparators to be single supplied.