How are Core iX names like Core i5, i7 related to Haswell, Ivy Bridge

Ivy Bridge, Haswell, etc. are code names taken during the development period of a new CPU architecture, which often corresponds to a generation of Core-i processors (and their Pentium and Celeron product lines with specifications even lower than Core i3).

And this is where the first few exceptions arise (smile after me):

• The code name Coffee Lake is used for both 8th generation and 9th generation Core processors.

• Different code names are used for the 1st generation Core processors, including Clarkdale (mid-end Core i3 / i5, as well as Pentium and Celeron of the same generation), Lynnfield (mid-high Core i5 and i7), Bloomfield (high-end Core i7), Gulftown (Core i7 Extreme) and Arrandale (mobile CPU), and potentially more.

  Despite having different code names, their microarchitectures don't differ much.

For this part, I assume we're talking about desktop processors (mobile processors have another whole load to talk about).

As explained perfectly in other answers, Ivy Bridge is the code name for the 3rd generation Intel Core processor family, and you'd expect Core i3-3240, Core i5-3670, Core i7-3770. The first number of the 4-digit "model number" usually is the generation number, with some exceptions:

• The 1st generation Core processor doesn't have a leading 1, so instead of Core i7-1920, you have Core i7-920 instead.
• For extremely high-end processors with their second number going up to 8 or 9, they belong to the "previous generation". For example, Core i7-4820K is a 3rd generation processor and has a code name of Ivy Bridge rather than Haswell.
  • This only applies to processors with their leading number ranging from 3 to 7 (i7-3820 to i9-7980XE)

Within the same generation, all CPUs have an identical microarchitecture, and usually come with related traits, for example CPI (cycles per instruction), on-chip cache arrangement, power consumption, PCIe bus support, and ISAs (with exceptions).

The name Core i3, Core i5, Core i7 are product names for processors targeting different markets, just like Apple's iPhone XS Max, iPhone XS and iPhone XR (all of them are the same generation iPhones with different specs and prices). Within the same generation, they're identified easily by the number of cores and support for hyperthreading (HT). For example, for all Core processors ranging from 1st generation to 7th generation, Core i3 has 2 cores with HT, and Core i5 has 4 cores without HT, while Core i7 has at least 4 cores with HT.

When comparing across generations, things start to get complex:

• All Core i5 processors up to the 7th generation (Kaby Lake) have 4 cores with no HT. However, 8th generation Core i5 increased core count to 6, which is kept with 9th generation Core i5 (still no HT).
• All Core i7 processors up to the 7th generation have 4 cores with HT (8 threads), and the core count increased to 6 with 8th generation Core i7. A drastic change is that 9th generation Core i7 processors have 8 cores without HT.
• Core i9 first appeared with 6th generation Core Extreme processors (the successor of i7-6950X is i9-7960X/7980XE), replacing the top-end i7 product lines.

I think mobile processors can't just be ignored this easily.

Contrary to desktop processors, mobile ones are heavily constrained by TDP, due to considerations of power supply, cooling as well as battery life, and as a consequence mobile processors aren't separated vertically the same way as desktop ones.

The first notable difference is that the first digit of a mobile processor always corresponds to a generation (as of now). That says, even if i7-6950X is a 5th generation desktop processor (Broadwell), i7-6970HQ is still a 6th generation mobile processor (Skylake). One same thing is that the 1st generation doesn't have a leading 1, so there comes i3-330M, not i3-1330M.

The key difference between desktop and mobile is their vertical segment.

• For all processors from 3rd generation up to the 7th generation, Core i7-H and i7-M (trailing letter) have 4 cores with HT
  • 1st generation Arrandale Core i7-M has 2C/4T
  • 2nd generation Sandy Bridge Core i7-M has 2C/4T or 4C/8T, identified by the existence of a trailing Q (Quad-core, this letter is used until Coffee Lake)
• For all processors up to the 5th generation, Core i5-H and i5-M processors have 2 cores with HT. For 6th generation and 7th generation, Core i5 H/M have 4 cores without HT. This is because up to Broadwell, 4C/4T would generate too much heat and eat too much power for a i5-level laptop, but with Skylake this is possible. However to keep the line clear between i5 and i7, Intel decided to remove HT from i5 processors.
• All Core i5 and i7 have "Turbo Boost", while i3 doesn't (the data "Max Turbo Frequency" is missing for all i3).

These "standard voltage" processors don't go below 35 watts with their TDP, and there are other product lines for needs of specifically low powers. They aren't directly comparable with standard processors (targeting low power & battery endurance vs. targeting performance).

• For processors ending -U, their TDP are either 15 W or 28 W, and always comes with HT (Intel Core processors, not Pentium or Celeron).
  • For processors up to 7th generation, all have 2 cores and 4 threads
  • For 8th generation Core i5 and i7, they have 4 cores and 8 threads (yeah, evolution of technology has made this possible)
• For processors ending in -Y, their TDP don't exceed 8 W so they can fit in thinnest tablets.

And honestly, I don't see many practical differences between i5-U and i7-U, except for a minimal difference in clock frequency. More important differences aren't identified by i5/i7, however, like integrated graphics (HD Graphics / Iris / Iris Pro, all of which can appear on both i5 and i7).

To sum up, Core-iX are different vertical segments of Intel's CPU product line, while code names are chronological iterations of CPU architecture.