How different is the first [X] rocket compared to the latest [X] rocket?

[intelliCom]

How different is the...

- Atlas D to the Atlas V?
- Thor-Delta to the Delta IV?
- Saturn I to Saturn V?
- Ariane I to Ariane V?

...and so on, as per title.

Does the latest version carry anything over from the very first? If so, what?

[Beccab]

For the second and third one:
- Nothing, the Delta III and Delta IV have next to nothing in common other than upper stage (which again isn't in common in the DIVH) - and at that point, you may as well call Atlas V, Titan IV and Shuttle-Centaur all part of the same family
- Again nothing basically, many proposed Saturn V payloads included the RL-10 used in the S-IV stage of the Saturn I but none of the flown ones did; the Saturn IB, however, shares a lot with it, given the S-IVB stages used in each of them are basically the same and share the J2 engine with the second stage. The clustered first stage, however, was always a dead end

[intelliCom]

1 hour ago, Beccab said:

- Nothing, the Delta III and Delta IV have next to nothing in common other than upper stage

Probably better to name the upper stage something and call the entirely new lower stage(s) something different to be less misleading. Rocket names can be real damn weird.

[UmbralRaptor]

The Atlas V has nothing directly in common with the Atlas D. The Atlas V does use a Centaur which is a direct descendant of the ones used on slightly more recent Atlases, and the Centaur itself has some heritage in the design of the Atlas D's first stage tanks. Not sure how to count that.

I'm not sufficiently aware of the Ariane rocket family's history to comment much. I was going to say that there's nothing, but since both the Ariane I and Ariane 5 have hydrolox upper stages, there's a chance...

[Royalswissarmyknife]

Some Versions of the Ariane 5 use Ariane 4 upper stage engines but other then that Ariane 5 is much different compared to its older counterparts

[Kermann Nolandung]

Ariane I to IV are quite similar. 
On Ariane V, only the HM7 engine (60 kN LH2/LOX) of the upper stage of the ECA variant is common.

The evolution from I to IV was rather KSPish, and it would be interesting to detail it.

To summarise the Ariane programme, the rocket was initially designed to send about 1.5 T (payload+AKM) into the GTO. 

During the previous programme, Europa, there were some developments (Europa III) to increase its payload. The first stage (called Drakkar), powered by 4 Viking engines (each 700-800 kN, powered by N2O4/UDMH) was to replace the Blue Streak stage and a new large second stage powered by an LH2/LOX engine was to replace the two upper stages.
The Viking engine is the descendant of the Vexin engines used on the first stage of the Diamant rocket and the second stage of the Europa I rocket.
The Europa programme failed and was reborn through the Ariane programme.

Ariane I is a three-stage rocket. 
The first stage, Drakkar, is retained. To reduce development risks, the new LH2/LOX engine is retained only for the third stage because it requires a smaller engine (HM7 60 kN). And the second stage consists of a single vacuum variant of the Viking engine.

Later, to increase the payload of the rocket, the third stage was lengthened.
To compensate for the lower initial T/W ratio of the first stage, in addition to the gradual increase in power of both engines (hydrazine is now added to UDMH to better stabilise the combustion), strap-on boosters were added. This is Ariane III.
Ariane II is only an Ariane III without boosters intended for a lighter payload and was to be launched with partially empty tanks even at full load if I am not mistaken.

Ariane IV is an Ariane III with an extended first stage and larger boosters (combination of solid and liquid fuel). The combinations are 40, 42P, 44P, 42L, 44LP, 44L (0: no boosters, P for powder, L for liquid).
The liquid fuel booster uses the same Viking engine as the first stage. 
The Ariane 44L variant is powered by 4+4+1 Viking engines and 1 HM7B engine and can send 4.9 t in GTO compared to 1.8 t with Ariane 1.

Ariane V is a different architecture with a main LH2/LOX engine (1300 kN Vulcain)and two large solid boosters. In the later evolution, ECA, the HM7B engine is used in the upper stage.

Ariane VI is similar to Ariane V with the Vulcain as the main engine. The solid boosters are common with the first stage of the Vega C rocket. 
But the upper stage is composed of a new, larger LH2/LOX engine (Vinci 180 kN) that can be restarted.
This engine was initially intended to equip the upper stage of Ariane V for its mid-life evolution.