Can someone clarify all these terms and their differences? And other questions


I am currently doing a quant rotation program in a big bank and I am trying to decide what would be best to choose for my last rotation. Thinking about this has led me to consider various buzzwords and I realized I don't understand the differences very well:
1)quantitative trading
2)algorithmic trading
3)e trading
4)electronic market making
5)automated market making

My understanding is that e-trading is the general concept of having an electronic platform where clients can trade (vs e.g. voice trading), but the trading decision itself may or may not be automated, thus 2 is a subset of 3. I know execution is about deciding how to split large orders to reduce market impact. Is this all there is to 2 as far as banks are concerned? Do banks actually have algorithmic pricers for deciding a mid price and a spread? Do 4/5/2 refer to the same thing? And what exactly does 1 involve? Is it an umbrella term referring to any type of quant work?

Some follow up questions:
- ML is all the buzz these days. Is it actually used in any way directly related to trading and P&L (ie not document analysis via NLP for instance)?
- Is there any type of quant that does something similar to what hedge funds do?
- What is the best type of quant if you aim, in the future, to try to get into a shop like Citadel?
- What is the best type of quant if you aim, in the future, to try to get into a shop like Citadel Securities?
You will receive different answers to those questions depending on who you ask.

Those 6 words are used interchangeably and have similar definitions. Some nuance- quant trading might mean anything related to statistical modeling used for trading decisions whereas algorithmic trading might mean a completely automated trading system that takes in data, applies a model, outputs trades (more narrow definition). E-trading is a word that became popular as the opposite of human trading (trading on the NYSE floor or CME pits where you physically say your trade). E-trading = electronic trading = sending an order to an exchange electronically via some protocol. 4) and 5) are very similar. 6) is similar to the above but a different area. Execution focuses on how your trades are carried out (time of day, VWAP/TWAP, order size, transaction costs, things like that).