This all boils down to fairly simple arithmetic. 1/48 scale and 1/4" = 1' most definitely do mean the same thing. There are 48 units of 1/4" in a foot.
1/144 scale is not the same as 3/32" = 1' (though it's close). There are 128 units of 3/32" in a foot. So 3/32" = 1' is the same as 1/128. 1/144 is the same as 1/12" = 1'. There are 144 units of 1/12" in a foot.
If I were you I wouldn't worry too much about whether a particular scale is an "architect's scale" or an "engineer's scale." About the only people to whom the distinction is relevant are the architects and the engineers - and they only worry about it when they go to the drafting supply store and pick out tools.
Scale doesn't need to be intimidating; it doesn't require any math beyond the grade school level. (If it did, I wouldn't be able to handle it.) Part of what confuses newcomers to the hobby, I'm afraid, is that experienced hobbyists have some bad habits in talking about scale. I cringe whenever I hear a plastic airplane modeler talk about "quarter scale." A model airplane on 1/4 scale wouldn't fit in his house. (What he actually meant was 1/4" = 1', or 1/48.)
To my notion the most useful tool in sorting out scale is a pocket electronic calculator that works in feet, inches, and fractions of an inch. (I'm assuming you're most comfortable working with feet and inches. If you prefer the metric system - all bets are off.) All that's necessary to convert a prototype dimension to a the scale of the model is to divide that dimension by the scale. (If you're working on 1/72 scale and want to know how big a particular piece of your model should be, just key in the size of the real thing and divide by 72. The calculator will give you the "model size," to the nearest 1/64". If you want to convert to the metric system, the calculator probably will have a key that will change fractions of an inch to milimeters in one stroke.) Such calculators used to be hard to find, but nowadays Sears, Lowe's, and Home Depot, among many other such places, sell them for between $10 and $20.
Hope this helps a little. Good luck.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.