He he CA, you certainly know your onions (tomatoes in this case) ;D
I get what you pointing out, I really do but, the biggest difference between paste and puree is consistency, and thus depth of flavour.
Tom paste is basically tom puree but double or triple strength. The consistency will obviously be dictated by the strength of the paste/puree. Paste is also better value for money and is why BIR's/TA's use them and dilute it to a much runnier consistency, more like ketchup or thin puree.
The Tomato Puree and Paste differ by the amount of Natural Tomato Soluble Solids. Tomato puree must contain 8% to 23.9% of "Natural Tomato Soluble Solids" , the paste must contain minimum of 24% "Natural Tomato Soluble Solids" So the high end spec of tom puree differs by 0.1% of that of the low end spec tom paste! So I will concede that the variances can be very different.
If we being honest, we're splitting hairs, paste or puree of a certain concentrate will work very well in your recipes. I would only be concerned if you started specifying "sun dried or roasted Tom paste" Then it would start to get complicated.
Good to see you active again CA. long may it last

Ray
