Answer:
The answer is really YES to both. At times Aaron was instructed to take Moses rod to perform a miracle, but at the same time the verses I included below show that Aaron too had a rod and at times God did miracles through this (like the budding).
Very good question…here are the verses that talk about Moses, Aaron and the rod(s) they used.
Exodus 7:10 And Moses and Aaron went in unto Pharaoh, and they did so as the LORD had commanded: and Aaron cast down his rod before Pharaoh, and before his servants, and it became a serpent.
Exodus 7:19 And the LORD spake unto Moses, Say unto Aaron, Take thy rod, and stretch out thine hand upon the waters of Egypt, upon their streams, upon their rivers, and upon their ponds, and upon all their pools of water, that they may become blood; and that there may be blood throughout all the land of Egypt, both in vessels of wood, and in vessels of stone.
Exodus 7:20 And Moses and Aaron did so, as the LORD commanded; and he lifted up the rod, and smote the waters that were in the river, in the sight of Pharaoh, and in the sight of his servants; and all the waters that were in the river were turned to blood.
Exodus 8:5 And the LORD spake unto Moses, Say unto Aaron, Stretch forth thine hand with thy rod over the streams, over the rivers, and over the ponds, and cause frogs to come up upon the land of Egypt.
Exodus 8:16 And the LORD said unto Moses, Say unto Aaron, Stretch out thy rod, and smite the dust of the land, that it may become lice throughout all the land of Egypt.
Numbers 17:6 And Moses spake unto the children of Israel, and every one of their princes gave him a rod apiece, for each prince one, according to their fathers’ houses, even twelve rods: and the rod of Aaron was among their rods.
Numbers 17:8 And it came to pass, that on the morrow Moses went into the tabernacle of witness; and, behold, the rod of Aaron for the house of Levi was budded, and brought forth buds, and bloomed blossoms, and yielded almonds.
Numbers 17:10 And the LORD said unto Moses, Bring Aaron’s rod again before the testimony, to be kept for a token against the rebels; and thou shalt quite take away their murmurings from me, that they die not.