Erosion moves bits of rock or soil from one place to another whereas Deposition is the process by which sediments settles out of the water or wind that is carrying it, and is deposited in a new location.
Deposition transports previously eroded sediments, which, at the loss of enough kinetic energy in the fluid, is deposited, building up layers of sediment. Link: (https://prezi.com/icu5otb61tun/differences-between-weathering-erosion-and-deposition/)
Erosion deposited on an upper floodplain or terrace is unlikely to move again anytime soon. The retention times within the stream channel vary, as streams during rainfall and flood events may dislodge, erode, entrain, transport and redeposit particles ranging from fine sediments to coarse bed load including boulders in high gradient channels or high velocity locations. Sediment movement in the channel is episodic, with most moving at bankfull channel forming flows due the increased frequency of these floods every year or two. So particle deposition may or may not be the end stop, depending on where it deposits and how much time is considered. In large rivers with high sediment loads, you might find some internet u-tube examples of time lapse of how channel changes with time at some specified location. A book on incised channels by Schumer, Harvey and Watson (about 1962?.) may be useful Reference. Much available on erosion and sediment in the literature.
According to definition of soil erosion of course deposition is not a part of soil erosion. Erosion refers to detachment of the material and deposition refers to settling of eroded material which the material could be remobolized and redistributed in secondary erosional phases.
As well said above, weathering, erosion, transportation and deposition are among the main factors of the perpetual cycle of material transfert among different parts of a given sedimentary basin... So depending on the natural factors variations, any deposits may by removed and displaced by dissolution, fragmentation thanks to waters, wind ... so there is rarely a final state in nature...
But it is more important to imagine the temporal and spatial scale of the process. For example the local and short time scale can be considered as a cycle which starts with weathering, transportation and deposition and again redetachment and redeposition and . . ..
It is better to use "redistribution" as the final phrase, so that the deposition can be locally inside the erosion process.
But if the given temporal and spatial scale is big enough to be considered globally, the deposition in the oceans is the end of the process, at least in short and medium time scales.
It is difficult to say deposition is end process as in case of hydraulic structures such as dams deposition occurs on upstream as a result on the downstream there is erosion to protect which we need to provide protection work.