What is the IEC and ANSI name for an AA battery?

An alkaline AA is IEC LR6 (R6 for zinc-carbon) and ANSI 15A. In Japan it is called 単3 (tan-san), and an old German trade name is Mignon. Its nominal dimensions are 14.5 mm diameter by 50.5 mm height.

Are CR2032, CR2025 and CR2016 interchangeable?

All three are 20 mm diameter 3 V lithium coin cells, but they differ in thickness: CR2032 is 3.2 mm, CR2025 is 2.5 mm and CR2016 is 1.6 mm. A thinner cell may not make contact, and a thicker one may not fit, so match the exact number when possible.

Is an 18650 the same size as an AA battery?

No. An 18650 lithium-ion cell is 18 mm in diameter and 65 mm long, noticeably larger than a 14.5 x 50.5 mm AA. It is also 3.6-3.7 V nominal rather than 1.5 V, so it is not a drop-in replacement. The AA-sized lithium-ion equivalent is the 14500.

What does the number in 18650 or CR2032 mean?

Both encode the physical size. 18650 means 18 mm diameter and 65.0 mm length. CR2032 means a lithium (CR) coin cell 20 mm in diameter and 3.2 mm thick. This metric size code is common to most cylindrical and coin cells.

Can I replace an LR44 with an SR44?

They share the 11.6 x 5.4 mm form factor, but LR44 is 1.5 V alkaline while SR44 is 1.55 V silver-oxide with a flatter discharge curve and longer life. In most low-drain devices they are interchangeable; precision meters and watches usually specify the silver-oxide SR44.

Reference

Battery Sizes & Types

Common battery sizes — D/C/AA/AAA/N, 9V, coin cells and 18650-class lithium — with IEC, ANSI and Japanese names, dimensions, voltage, capacity and chemistry.