'A year' can be any year without any specification. But 'the year' means a particular/specified year or the one which is already mentioned and thereby known. E.g: In a year there are twelve months.

Context Explanation

(means any year or all years) I was born in the year 2000. (in that particular year) Grammatically 'a/an' is known as indefinite article and 'the' is definite article. The indefinite article (a/an ... The world’s oldest living cat has turned 30 years old.

Insight Material

According to the US New York Post and others, Flossie, the world’s oldest living cat residing in the UK, celebrated her 30th birthday on December ... Ten year old may be used as an adjective, but only attributively ("a ten year old boy"). And your last sentence is back to front: ten years old is an adjectival phrase like brainy, while ten year olds is a noun phrase like a boy. Is this the correct spelling of year's in this context? I'm not a native English speaker/writer, but I do consider myself fluent, and this spelling tickled something in the back of my brain.

Final Conclusion

If it matters, the report format only displays a maximum of two years at a time (this year, and last year).