Well, the "quick answer" is this:
LDS church (aka meeting house, stake house [unfortunately], stake center, etc.): the place where congregations attend weekly sabbath worship, as well as "community centers" for weekly activities, youth, boy scouts, women's org, priesthood (men's organization), blood drives, etc. A ward building will usually have two or three wards (congregations) meeting in it. A stake center will also usually have two or three wards meeting in it, but will also have facilities for a stake presidency and high council to meet. a ward is kind of like a parish and a stake is kind of like a diocese, i.e., a regional area comprised of several wards and branches ("little wards"). This is comparable to any other kind of church.
LDS Temple: This edifice (there are over 110 in the world now in operation) is never open on Sunday (or whatever the local Sabbath is). It is the location in which special, specific sacred ordinances are performed for the living, and also by the living for the dead. These are "one-time" per individual ordinances, sort of like baptism.
The things that take place in each type of buildings are all crucial to our beliefs--the church is kind of like the "everyday" and going to the temple is "extra", more sacred, a special opportunity, etc.
Since you are Jewish, perhaps the appropriate comparisons would be between the synagogue (regular meeting place) and the temple--at least traditionally, where the people went annually to offer sacrifice (I'm assuming I have this right--I am uninformed about how/if this has evolved to the present day).
I'm interested in your neighbor's understanding of the situation. It is exceedingly unlikely that they will convert the church into a temple. That has only been done once, with a historical meeting place in Utah, and from what I understand they plan on absolutely NOT doing that again ... Although it's very cool that they did it. It is also impossible to designate any given temple on the East Coast as THE primary east coast temple. I would estimate that if such a thing did/will exist, it would be the Washington DC temple, which is about 30 years old, and is already there. They are building so many temples in so many areas, there are the following, just off the top of my head: Palmyra (near Rochester and me
), one in White Plains NY, which I believe is somewhere north of NYC, Boston, DC, Atlanta, a couple in Florida, one in Connecticut, at least one in somewhere like Raleigh-Durham, etc. There are more than this, but this is what I can think of.
What is likely, and increasingly likely, is that there will be a small temple built on property adjacent to the meeting house. There are more and more being built like that, and they often use each other's parking for busy days, i.e., when there is a stake conference the people use the temple parking on a Sunday, and when people are doing sessions at the temple on a busy Saturday, they might use the church parking lot. The church is really trying to assess property it already owns in cities and countries around the world.
Okay, that wasn't quick, but I always have lengthy replies, and hopefully it gives you the info you were looking for. You could always have just read the first half and gotten the answer ...