Can you find a source for that? I've previously linked to Phil Spencer saying that first party game is anything they publish/fund.
Edit: Hell, Insomniac is even introduced as a "first party partner" at MS E3 2013.
Aside from Wikipedia, and how you feel about Wikipedia entries, no, not really:
http://en.wikipedia.org/wiki/Video_game_developer
2nd Party development doesn't technically exist either as it's just 1st Party development with a slang term. Killer Instinct on Xbox One would un-officially be called 2nd party as, even though Microsoft owns the IP, the majority of the work is done by a third party they do not own, even though Microsoft likely has a good portion of creative control.
Basically, it works like this.
1st Party Developer - owned by the console manufacturer that makes games specific to that console manufacturer's hardware (i.e. 343 Studios/Halo for Xbox, Naughty Dog/Uncharted for PlayStation).
"2nd" Party Developer (still first party) - not owned by the console manufacturer that makes games specific to that console manufacturer's hardware and that console manufacturer owns the IP. This is like Metroid Prime or Donkey Kong Country Returns developed by Retro for Nintendo's platforms. Nintendo owns Metroid and Donkey Kong, but they don't own Retro. This is Iron Galaxy working on Killer Instinct, despite not owning the IP, but not being owned by Microsoft. This is Sumo-Digital, not owned by Sony, but worked on Little Big Planet 3.
3rd Party - typically this is an IP not owned by the console manufacturer and typically not published by a console manufacturer. This is the majority of games - like the upcoming Batman: Arkham Knight which is owned by Warner Brothers and being developed by Rocksteady (neither of which are owned by any of the console manufacturers). 3rd Party Exclusives are exclusives owned by that developer (or separate publisher) specific to one console (and/or PC).
Dragon Quest Heroes, coming to PS4 later this year on October 13th, is a 3rd party exclusive. The IP is not owned by Sony, nor was it developed by Sony. However, Bloodborne, which came out in April, was developed in tangent with Sony Japan and From Software (a development company Sony doesn't own), though Sony owns the IP entirely making Bloodborne a first party title. Sunset Overdrive, despite being funded by Microsoft, is owned wholly by Insomniac - Insomniac can take that IP and put a sequel (as I don't know the conditions of the agreement) on any platform it wishes, but if it were a first party title (i.e. owned by Microsoft), there would be no way that IP would see the light of day on any other platform. Rise of the Tomb Raider, whether it's timed or not, isn't a first party title (even though Microsoft is publishing it) because the IP is owned by Crystal Dynamics which in turn is owned by Square Enix, neither of which Microsoft owns.
Clear as mud, right?