The full doctype is only used by browsers for switching between quirks and standard mode. Any docytpe will trigger standards mode and so get the browser displaying the page as close to the standards as the browser is capable.
The doctype itself is only used by validators in order for you to validate whether your HTML complies with a given standard to at least the extent to which the validator is capable of checking (there are some rules the valudator can't check).
So an HTML 4 strict doctype validates that you only used HTML 4 tags.
An HTML 4 transitional doctype checks that you used HTML 4 and HTML 3.2 tags
An HTML 3.2 doctype checks that you used HTML 3.2 tags.
An HTML 2 doctype checks that you used HTML 2 tags.
In each case any proprietary tags you use will be reported as an error as will any tags not in that version of HTML.
If you are not planning on running your code through a validator you may as well use the short version of the doctype <!DOCTYPE html> as that is a valid doctype for all versions of HTML from 2 through 4 and is the only part that the browser needs for its mode switching.
HTML 5 which is reverting to the HTML 1 days of not being based on SGML and therefore not having an SGML doctype has declared that in that version of HTML the <!DOCTYPE html> tag is an HTML tag used soley for mode switching in browsers. That allows it to continue to be compatible with the way that browsers use that SGML tag in HTML 2 through 4 for mode switching.