As always with these discussions you need to go back to 1922 and the Washington Naval Treaty.
WNT was focussed on battleships, carriers & large cruisers. It left destroyers alone. Britain (Admiralty S & T, V, W,Mod W and their equivalent Leader classes) and the US (4 stackers) had plenty of destroyers left over from WW1 so that new construction wasn't needed immediately. Japan built a series of equivalent destroyers. Japan continued with developing its line of WW1 through to the mid-1920s. France & Italy need to be considered separately and I'll return to them in later.
Britain started planning renewal of its destroyer fleet in 1923 with orders for 2 prototypes in 1924/25, followed by a flotilla of 8 plus a slightly larger Leader each year from the 1927 Programme through to the 1935 Programme (the A-I classes. The 1930 C class saw only a leader and 4 ships). These showed incremental improvements year by year with some fitted out with minesweeping gear or ASDIC and some for minelaying. Effectively slightly larger developments from V & W class. The last of these was completed in Jan 1938.
Japan rocked the boat in 1926 with the development of the "Special Type", the Fubuki class, 1,750 tons standard, with 6x5" in enclosed twin gunhouses & 3 triple 24" TT. 24 ships laid down between June 1926 and March 1930 for completion June 1928 to March 1933, followed by 4 Akatsuki class.
London naval Treaty 1930 signed April 1930 Part III (to which only the US, Britain & Japan were signitories).
This sought to limit the size & number of destroyers for the first time, both in terms of size of individual ships and overall destroyer tonnage. So Britain & the US had 150,000 tons of destroyer standard tonnage and Japan 105,500 tons. While individual ship size was limited to 1,850 tons standard, they could only devote 16% of their tonnage to ships of 1,500-1,850 tons (24,000 tons for Britain & the US or 13 ships while Japan was entitled to 16,800 which it was already exceeding so couldn't build any more over 1,500 tons in the short term.)
Japan.
Tried to squeeze a quart into a pint pot with its next class cutting the 5" armament to 5 guns (2x2 & 1x1) and taking out a set of TT. 6 ships built. And then they ran into stability problems as highlighted in the Tomozuru incident causing them to be redesigned, as were the following class (10 ships) so that they slightly exceeded the 1,500 ton limit.
By the time Japan got round to laying down the next class, it had already given notice in Dec 1934 that it would be leaving the Treaty system on 31 Dec 1936 and the next destroyer class, the Asashio class, wouldn't be completing until 1937-39 so they built them bigger (c2,000 tons standard), along with the following Kagero class. Everything after that was laid down after the outbreak of WW2 in Sept 1939.
USA
Was late to the game of building new destroyers. It began in 1932 with the Farragut class, the first of the so called "Goldplaters", of 1,365 tons standard. Subsequent classes built on that, switching to a single funnel design in 1935 with the Gridley class and increasing the TT armament to 16 tubes. The last of these were the Sims class (12 ships) laid down in 1937-38 only 3 of which completed before the outbreak of WW2. The Sims were the first US destroyers to be fitted with the Mark 37 director system, but only carried 12 TT as designed. There were 73 of these "Goldplaters"
In parallel to those 1,500 tonners the USN built the Porter (4 twin 5" & 8TT) & Somers (4 twin 5" & 12 TT) class destroyer leaders of 1,850 tons standard. But note the guns fitted in these were single purpose low angle mounts. That was the cost of increasing the number of guns. There were 13 of these ships laid down 1933-36, a number that met the requirements of the 1930 Treaty.
The last pre-war designed destroyers wer the Benson-Gleaves class, where the tonnage increased slightly over the Sims to allow a unit machnery arrangement. While the first of these were authorised pre-war, only 14 had been laid down prior to WW2. with the first completions from mid-1940. Repeat orders were made from 1940 due to delays with the Fletcher programme. These completed with a reduced armament due to topweight issues.
It was the need to rapidly renew the USN destroyer fleet that caused the USN to persist with developments of the Treaty limited classes through the Sims & Benson-Gleaves classes.
The Fletcher class therefore represents the first of the Treaty unlimited destroyers. Evolution of this class began in Autumn 1939, after the outbreak of WW2.
Britain
Faced with the prospect of fighting the Japanese Fubuki class, the RN examined its destroyer needs in early 1935. Out of that came the big 1,854 ton standard Tribal class, which traded torpedo armament (1 quad set) for more guns (4 twin 4.7") and a quad pom-pom to improve its AA armament. The first 7 were ordered in March 1936 and another 9 in June under the 1935 & 1936 Programmes. These completed between April 1938 & March 1939. But they were seen as a special type initially, the flotillas being referred to as the 1st & 2nd Tribal Destroyer Flotillas before being renumbered as ordinary destroyer flotillas in 1939. There was no separate larger leader for this or subsequent classes.
But the reduction in torpedo armament wasn't well regarded, so the succeeding J class (1936 Programme) was for a smaller ship 1,690 tons with 3 twin 4.7" but 2 quintuple TT. These completed from April 1939, with the last on 12 Sept that year.
The 1937 Programme saw the K class as a repeat of the Js (completed Aug-Dec 1939) and a new design in the L class with a new model of 4.7" gun (firing a heavier 62lb shell) in a fully enclosed gunhouse (with awkward ammunition supply and still low angle although increased to 55 degrees).
The next destroyers were ordered under the 1939 Programme. Here cost was becoming an issue. The M class were ordered as a repeat of the L class and, rather than a new class of even larger ships, the N class were ordered as J/K design for speed of construction, all being laid down July-Sept 1940 before any of the M class and the last of the L class.
France
From Washington the French built two types of vessel normally thought of as destroyers, with the role of the Contre-torpilleur not being that of a traditional destroyer.
Firstly the 1,300-1,400 ton Bourassque & Adroit classes laid down 1923-26 and completed up to 1930. The 1,800 ton Le Hardi class laid down from 1936 should be considered the successors to these, built to be faster to allow escort of the new capital ships.
Secondly the various Contre-torpilleur classes. Their role was more akin to that of British light cruisers in WW1 - supporting the fleet with tactical scouting and screening and anti-destroyer work. Designed for a war in the Med where speed (35.5-39 knots depending on class) and hitting power (5x5.1" in the first class then 5x5.5" in subsequent classes and finally 4 twin 5.5" in the Mogadors) were seen to be more important than endurance & staying power. They would work in divisions of 3 to tackle any enemy cruisers that they might encounter.
Italy
As I've noted on other threads, the French and Italians had their own little naval race inter-war. So the Italians responded to the French with the large Esploratori if the Navigatore and other classes and light cruisers. They also built small 1,000-1,200 ton torpedo boats. But again stability problems forced a move to larger sized vessels of the Maestrale, Oriani & Soldati classes of 1,600-1,850 tons with main armament of 2 twin 4.7" plus a couple of single 4.7" starshell guns and two triple TT.