Surfaces certainly have a topology (potentially more than one), surfaces are examples of one kind of a topological space, in fact the next interesting one after a curve. So I will not be surprised at all with co-occurrences of 'surface' and 'topology'. But surfaces and topologies mean different things.

Dogs have fur. Dogs are an example of a furry animal. But dogs and furs are not the same thing although they may appear in the same text often.

Topology is a traditional as well as an active branch of applied and pure mathematics, well, Physics too.

It has tons of text books printed on it, has several active journals and conferences dealing with it. https://www.amazon.com/s?k=Topology&sprefix=topology+%2Caps%...

Surprise, surprise ...not ...has an extensive Wikipedia page.

https://en.m.wikipedia.org/wiki/Topology

Math magazines for high schoolers have articles on it. Colleges offer multiple courses on it. Some of those courses would be mandatory for a degree in even undergrad mathematics.

If one wants to do graduate studies then one can do a Masters or a PhD in Topology, well in one of it's many branches.

It's also not a new kid on the block. It goes back to ... analysis situs ... further back to Leibniz, although it began to crystalize formally after Poincare.

If someone wants to use the phrase 'differential calculus' to mean something else in their love letters and sweet nothings, that's absolutely fine :) but in Maths (and Machine Learning, well, with quality of peer reviewing this might soon be iffy) it has a well established and unambiguous meaning.

Note because of its shared beginning at the feet of Leibniz, comparing it with calculus is not an unfair comparison.