Jamming and improvisation share common ground but they are like music and noise. Music can be thought of as noise but it is not noise, it can be a sheet of paper with notes or performed within subconscious thought. Noise can be music but it is not music, it can be just noise (although Frank Zappa would have probably argued this with some cosmic perception of reality).
The definition of improvisation is to perform something without preparation or without a plan. What they are referring to there is strictly the act of improvising, what you play (irrespective of the accompaniment, such as backing tracks) is the improvisation.
This gets fuzzy when you consider that most improvisation (with other musicians or backing music) uses a prepared theme like a key (eg. A minor) or a beat (eg. 4/4 120bpm). This would be called a jam session but the improvisation is anything played during the jam that was made up on the spot.
Jamming is not a type of improvisation, to 'jam' means to play with others, it's an exercise that brings the musicians together (like sticking bread together with jam). Jamming implies that the musicians are learning each others musical style in the process, building their relationship (musically speaking) with one another. Jamming will probably include improvisation but jamming is not improvisation.
Also note that because of slang usage of the (slang) term, jamming can also refer to a musician on their own for example "he has been jamming in his room all day". This would refer to the musician jamming (building the relationship) with his music or instrument rather than other musicians.
To summarize the confusion in detail:
Jamming usually consists of some improvisation where the music is made up spontaneously as it is played. The opposite could be a rehersal and thought of as "practicing" where a specific piece or song is played through by everyone.
Improvisation can be referred to as jamming when talking about the growing bond between the musician and music (here music refers to a song, musical theme, other musicians, or instrument) or where the music sounds unprepared.
Everyone jamming could be improvising at some point but they could also be practicing a set piece with no improvisation.
You improvise, you make it up.
You jam, you gel with external sources of music.
both imply the inclusion of some kind of unpreparednesses.
It's not vague at all, it's clear as mud.
Edit: to attempt to answer your questions
Some say that improvisation is one player making up melodies over established chord sequences
I've played for years in bands and we all improvised at the same time, every time we got together, to see what ideas come up for new material. I think they're just saying that's one way to improvise, if that's their final and complete definition of improvisation then I'd suggest they get out of the house a little more.
jamming is starting from basically nothing, and each player adding their own part to the ensuing jigsaw.
that's the standard jazz configuration, the group holds a scene and they take turns trying to pull everyone off course. the idea is that a jazz band should put faith in whoever is improvising, faith that they will bring it all back together somehow before the next persons turn.
yes, think i covered that earlier
edit: the only percieved similarities are when we're talking about a session where that "session" could be called both an improvisation and a jam. It can also be said that the musicians in a session are jamming and/or improvising.
could one finish playing in an ensemble situation, and say 'that was a good improv', or 'that was a good jam' with any exactitude?
probably, if any of it was improvised then it could be called a good improv.
jam could always be used because even a performance is a way to gel with the group.
would it be fair to say one (or both) are applicable to any particular genres? or definitely not, as the case may be?
not a chance. it is used everywhere
it's really confined to jazz
no, not confined at all, it just originated from jazz. as did the term gig which was derived from engagement meaning engaging with an audience. I've been to a few metal gigs, sure you could argue there's always at least some influence that jazz has on metal but... you get my drift
Dictionary definitions are also mixed and vague on the issue.
They're pretty spot on, it's where the definitions use the other term that's confusing maybe. Example the term jamming will have the word improvisation in its definition and vice versa.