Old CS1 explanation is good. What we're dealing with are basically brand names and parts binning.
Since the difference in microprocessors is usually hard-coded and fact-based, wikipedia does a good job explaining the differences. Celerons typically have less cache, and some features disabled on purposes to create a low-end market, or, rather, not to disturb the high-end market. In other words, give a reason to have a high-priced product. Celerons may have things like turbo-boost, and AES, hyperthreading, VT-d, and more, deactivated. Slower bus.. The transistors are there, but turned off. And today's Pentium bears little resemblance to the Pentium 60 and 66 from back in the day.
Intel has main 5 tiers of X86 today:
..ranging from lowest to highest in performance. And things to consider when shopping aren't all that different from the old days. Clock speed, cache, # of cores, special instruction sets like MMX, and integrated graphics.
My P3 rig is really a P-III Celeron, 1400MHz with 256K L2 cache and 32K L1 cache, 100MHz bus.
If it were a "real" P3 it would have a 512K cache and a 133MHz bus.
I specifically chose that to keep with the 100MHz BX chipset bus and overall system + memory stability. It was the right choice.