Look at marketing ideas another way and you have a better understanding of what search tries to accomplish.
Look at search another way and you have a better understanding of marketing.
The size of a market is the number of people selling and buying.
If you publish a book, then from your perspective the market size is anyone who buys books.
FOR SEO: How large is your market? How many people are buying (searching) and how many people are selling (publishing)?
The addressable market is the group of people who might be interested in what you're selling.
It's the group of people in the market that you can sensibly talk to.
If you publish a book on link building, the addressable market would be anyone interesting in online marketing and search engine optimization.
FOR SEO: There are a lot people (searchers) on your market but which are the addressable ones? What's the widest net you can cast that the catch still would make sense? Consider user personas at this stage.
The target market are the people in your addressable market that are likely to buy from you.
If you write a book on link building, you're writing it for a specific group of people: newbies, advanced link builders, SMB owners, CEO's, ad agency people, in-house SEO's, or whatever group.
FOR SEO: Who is your audience? Who are you really, primarily, at the core, talking to? What keywords do they use? What would they search for? What problems are they trying to solve?
The market share is the group of people in your target market expected (hoped, estimated, projected)to buy what you sell.
If you sell a book about link building, aimed at beginners, then some people in that group will buy your book, some will buy someone else's book, and some may skip buying altogether.
Another way to talk about market share is as demand: how much demand is there for your offering?
FOR SEO: Given everything about your market -- available offerings, players, money spent on getting customers, etc. -- what is the amount of searchers you can expect to go for your result versus another? Why?
Limited Scope Example: The Farmer's Market
You sell strawberries on your town's farmer's market.
Everybody selling on the farmer's market this week and everybody there with money to buy something form the market's size.
The addressable market are the people there to buy fruits or vegetables.
The target market for your strawberries are those people in the addressable market (everybody there, with money, who wants to buy fruits or vegetables) who want to buy fruit in general and strawberries in particular.
Your market share will be the number of people wanting to buy strawberries that end up buying from you.
SEO Example: Keyword Research
The number of queries for your keyword ("cheap hotel New York") and the number of results are the current market size.
The number of people who are actually and doing these searches now and are looking to book a hotel or are planning a stay in New York in general, that's your addressable market: the group of searcher interested in your message.
Within that group is a group of customers you have in mind. Seniors? Young folks? Backpack travelers? Overnighters? People who plan their vacation around Internet access?
These searchers are your target market.
The number of searchers that come to your web site based on your targeted keyword are your (market) share of the pie.