Your first picture is a Gearing Class Destroyer, before alteration. There is no number on the bow, so I'm assuming that it is also the USS Bordelon DD881, but if not it's still looks to be a Gearing Class Destroyer, on in sailor talk, a "tin can" or just a "can" The Bordelon was launched in 1945 and transferred out out of the US Navy in 1977, and given to Iran, also in 1977 where it was scrapped for parts.

The photo is of a Gearing Class tin can as built, but by 1959 there 44 left that looked like the original. The rest were converted and ended up with the removal of on forward twin five inch gun mount, and the mast replaced with a heavy duty one to handle new electronic gear, and the bridge was remodeled. Compare the pictures,

This is what the Bordelon looked like after the alterations, and appears to have been done in the stern view of the ship.
The following is probably more information than you ever wanted to know about a Gearing Class Destroyer.
A brief description of a typical Gearing Class destroyer:
- Compliment = Normal 274 (14 Officers and 260 Enlisted) and wartime 345 (20 Officers and 325 Enlisted).
- Dimensions = 390'6" x 40'10" x 14'4" draft.
- Fuel capacity = 196,000 gallons.
- Range = 5,800 miles at 15 knots.
- Propulsion = Simply 4 boilers supplying 2 sets of turbines generating 60,000 s.h.p. to 2 shafts each with a 12.5' four-bladed propeller.
- Speed = 34.5 knots.
- Weapons = 3 - 5' 38 cal. twin gun mounts, 2 - quadruple 40mm gun mounts, 2 double 40mm gun mounts, 10 - single 20mm gun mounts, 2 - quintupled 21" torpedo tube mounts, 2 - depth charge release racks, and 6 - single K-gun depth charge throwers.
Soon after commissioning, most of the early Gearings traded their aft torpedo tubes for an additional quadruple 40-mm gun mount, and this change became standard for those still under construction. The navy also converted a number of the Gearings to radar pickets (DDR), in which case, each ship’s forward torpedo tubes were replaced with a heavy tripod mast to support an SP aircraft height-finding radar and various electronic warfare antennas.
The Gearing DDE's made an ideal platform to test new ASW weapons and sonars that the Navy was developing. Operational experiences gained from these DDE's, aided the Navy in developing ASROC - Antisubmarine Rocket and DASH - Drone Antisubmarine Helicopter. The longer Gearing hulls would provide an ideal platform for these new weapons, but the ships were aging and in need of major re-construction and overhaul.
By 1959, only 44 origional Gearing class destroyers had not been converted into either dedicated submarine warfare destroyers (DDE), hunter-killer destroyers (DDK), radar picket destroyers (DDR), or for special research.
The Secretary of the Navy instituted the FRAM (Fleet Rehabilitation And Modernization) program. Only 49 Gearings of all types were scheduled for this program. On May 1, 1959, the Perry DD 844 was the first Gearing to commence the FRAM MK 1 conversion. Perry's conversion was completed on April 1, 1960 at a cost of $7.7 million.
The basic FRAM MK1 reconstruction consisted of the following:
- Below the main deck, all machinery and systems were either overhauled or replaced.
- Above the main deck, a new superstructure.
- Installation of ASROC
- Installation of DASH hanger and flight deck.
- Installation of the SQS-23 SONAR and dome.
- Installation of SPS-29, -37, or -40 air-search radar.
- 2 - MK-32 triple torpedo launchers.
- All topside machinery being either overhauled or replaced.
The FRAM MK1 program had two variants. They were as follows:
- Group A - The loss of mount 53 (aft) and the inclusion of MK10/11 Hedgehogs on each side of the bridge and the MK-32's located aft.
- Group B - The loss of mount 52 (forward 01 level). The inclusion of a practice 5" loading machine and the MK-32 both on the forward 01 level. They also recieved a larger ASROC and torpedo storage area.
There was also FRAM II, but that was mainly to update, overhaul and/or replace SUMNER class ships systems and machinery.
At the end of the FRAM program, 80 Gearings had recieved FRAM MK 1 conversion, while 15 were updated under FRAM MK II. FRAM added approximately 15 years of service to Gearing Class destroyers. Only a couple remain in foreign navies and one Joesph P. Kennedy Jr. DD 850, has been preserved as a museum.