Definations vary, depending from who you ask. Noisecore for me, and most of people I know, is the style created with blast beat or chaotic drums, chaotic guitar & bass noise and vocals. Often hardly at all riffs and length of tracks remains in couple of seconds explosions where maximum amount of energy is included in minimum amount of time. Tracks can go to even couple dozen of seconds, but hardly ever reaches length of 1 minute or so. Before this also very noisy hardcore & punk bands such as Disorder, Kuolema and others used "noise not music" slogans, but still remaing more hardcore than noise.
But noisecore as explained before has been use as a term since mid/late 80's and stabilized itself as a own genre. After that noisecore term has been during the years adopted by different people to describe also other forms of music. Some consider dull grunge with feedback to be "noisecore". Maybe as answer to "noiserock". More recently some semi-mainstream music what is actually technical metallic hardcore, has get stamp of "noisecore" from mainstream metal magazines like Terrorizer. But simply, if it's music, it's not noisecore! Those people probably never heard of noisecore. Journalists and fans who claim Isis, Burnt by the Sun and the Luddite Clone etc to be noisecore can just fuck off and find term for the music what doesn't exists yet. I have been told bands themselves have not used this to describe themselves.
Very often noisecore includes some musical elements, but they serve as mere "intro" before actual blasting insanity. Some of the bands play noisecore because of lack of skill, but it is important to notice that the genre is not only a joke or field for "untalented", but also serious form of "music"?
Grind-noise is pretty much the same thing, but goes closer to grindcore, including some grinding riffs, sometimes song structures, but still closer to noisecore than "musical" grind.
These days grindcore is not what it used to be. Before grindcore term was know, there was fast hardcore and metal bands doing recordings and they were dirty and rough. When term grindcore was better known, bands like Repulsion, Napalm Death, Blood, Unseen Terror, Agathocles and countless others played music what remained harsh, noisy and brutal. Mince riffs, blasting drums, brutal vocals and usually short and to-the-point tracks.
These days many of the grind bands are over-produced and technical. Some, including the music press, seems to accept music as "grindcore" if there is fast blasting drums. Fast drums alone doesn't make music grind! Sometimes you get talented guitar leads, amazingly fast blast beats, technical riffing and melodies and surely it is good for those who just switched from Slipknot to the semi-underground. But for those who desperately crave for good old grind atmosphere, many of todays offerings remain disappointment - if not even disgrace to the term grindcore! This site is not interested to involve in such type of "grind".
Noisecore/grindcore doesn't have standard imagery, ideology or lyrical content. Underground attitude and noncommercial way might be one of the very few standards of the genre. In ideology or expression, each form of life and death is represented. Some for bigger, some for smaller extent. Noisecore and grind is melting pot of people from metal, punk, industrial, experimental, (etc) scenes. This lack of universal image can be seen as a good thing. Within most music styles, there is stereotype way of life or thinking and therefore, to be "accepted", people make articifial images what fits in it. With noisecore/grind there is no need for that, and this makes bands more honest. You see easier who is politically motivated to certain direction, who is peace lover, who praises war and violence, who celebrates the gory orgies in excrement and who is there just for fun. Just pick the directions you enjoy and leave the rest.