Differentiating 'peat' from 'smoke'

Alright. Slowly, but surely, I am trying to build some awareness into my palate as I adventure through the land of single malts. I am interested in expanding from the Speysides and Highlands into territory that borders on Islay and am trying to plot an appropriate migratory path. One thing I struggle with is trying to define the difference between 'peat' and 'smoke'.

It seems to me as though these are sometimes used interchangeably when I try to do research via Google, but perusing the FAQ seems to indicate that they are also different. In that it seems like things that are heavily smoky tend to also be peaty, yet somehow you can get some level of peat without the smoke. What would I be looking for in the nose/taste/finish for something that is peaty, but not smoky, and conversely, smoky but not peaty?

For example, I had the opportunity to sample a dram of Macallan 25 at a vertical tasting last year. While it was somewhat milder/smoother than say, a cask strength or Macallan Sherry 18, but unlike all other (younger) Macallans that I've tasted, this particular pouring of the 25 had a 'smoke bomb' finish that would just erupt in the throat, mouth, and nose about 3-4 seconds after taking a sip. It tasted precisely like I had inhaled a mouthful of campfire smoke. Is this 'pure smoke' or would there be peaty aspects to this?

Perhaps someone could guide me towards something that would have differences in the two flavours/sensations so I could try to learn how to pick them out. Currently I have to hand:

Aberlour 10, Balvenie Doublewood 12, Glenlivet Nadurra, Macallan Cask Strength. In the past, I've sampled Macallan 10, 12, 15 (Oak), 18, 25. I've had a bottle of Glenfiddich 15.

I also have access to a local with a truly prodigious selection of whisky, whiskey, blends and malts, so if there is a couple things to try I can certainly spring for a dram or two for experiments instead of a whole bottle if it would aid in building appreciations.

TL;DR: How do I identify a 'peat' taste in contrast to 'smoke'?