map projections vs. coordinate systems

[Sharif Razzaque]

Subject: map projections vs. coordinate systems
Hi,
    I've been reading these mailings for a while and I'm getting really confused about the map projection discussions.  Could you please read my following assessment and let me know what you think?
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   There is a distinction between a coordinate system & a map projection.  Different coordinate systems are different ways of referring to the same points on the earth .  On the other hand,  different map projections are just different ways of displaying the earth  For example, New York has the same lat. & long. (a coord-system) whether we look at a Mercator, Orthographic, Sinusoidal Equal Area, or Lambert Conformal Conic projection.  
   It seems that GRASS does NOT display maps in different projections.  The programs such as v.proj actually convert maps from one coordinate system to another (i.e. from lat/lon to state-plane).  Would you say this is accurate?
   Now what really confuses me is that these mail discussions & GRASS itself uses the word `projection' in situations where `coordinate system' seems more appropriate (like with v.proj). Even worse, I have seen mail that talks about transforming maps from lat/lon to mercator or lambert conic. Lat/Long is a coordinate system (which tells us nothing about how to display it), while mercator is a projection (which tells us nothing about which coordinate system to use). 
   Is my understanding of projections & coordinate systems right? Furthermore, does GRASS indeed use the word `projection' the wrong way?  Please let me know what you think or if I'm on the wrong track.  Thanks in advance!!

  Sharif Razzaque
	  sharif at lams.msd.lmsc.lockheed.com
  phone: (408) 756-4358 & 756-0494