I would like to know if Sam and Frodo wore the same clothes during their entire journey to Mordor.
They did not
The fellowship are given new clothes in Lothlorien
The Elves next unwrapped and gave to each of the Company the clothes they had brought. For each they had provided a hood and cloak, made according to his size, of the light but warm silken stuff that the Galadhrim wove. It was hard to say of what colour they were: grey with the hue of twilight under the trees they seemed to be; and yet if they were moved, or set in another light, they were green as shadowed leaves, or brown as fallow fields by night, dusk-silver as water under the stars. Each cloak was fastened about the neck with a brooch like a green leaf veined with silver.
The Lord of the Rings Book II - Chapter 8 "Farewell to Lórien"
At Cirith Ungol Frodo is captured and stripped. His clothes are all sent off to Barad Dur and he and Sam adopt orc clothing when they leave, which also helps them blend in.
He opened the bundle. Frodo looked in disgust at the contents, but there was nothing for it: he had to put the things on, or go naked. There were long hairy breeches of some unclean beast-fell, and a tunic of dirty leather. He drew them on. Over the tunic went a coat of stout ring-mail, short for a full-sized orc, too long for Frodo and heavy. About it he clasped a belt, at which there hung a short sheath holding a broad-bladed stabbing-sword. Sam had brought several orc-helmets. One of them fitted Frodo well enough, a black cap with iron rim, and iron hoops covered with leather upon which the evil Eye was painted in red above the beaklike nose-guard.
'The Morgul-stuff, Gorbag’s gear, was a better fit and better made,’ said Sam; 'but it wouldn’t do, I guess, to go carrying his tokens into Mordor, not after this business here. Well, there you are, Mr. Frodo. A perfect little orc, if I may make so bold-at least you would be, if we could cover your face with a mask, give you longer arms, and make you bow-legged. This will hide some of the tell-tales.’ He put a large black cloak round Frodo’s shoulders. `Now you’re ready! You can pick up a shield as we go.’
The Lord of the Rings Book VI - Chapter 1 "The Tower of Cirith Ungol"