Dalton's states that the sum of the partial pressure in a mixture of gases will equal the total pressure.
\[\eqalign{ P_{\rm total}&=\sum_{i=1}^n {P_i}\cr &=P_1 + P_2 + \cdots\cr &={{{n_1}RT}\over{V}}+{{{n_2}RT}\over{V}}+\cdots\cr &={({{n_1+n_2+\cdots})RT}\over{V}}\cr &={{n_{\rm total}RT}\over{V}}\cr }\]
This is often shown in the following way:
\[P_{\rm total} = P_{\rm A} + P_{\rm B} + P_{\rm C} + \cdots \]
So what this shows you is that the total pressure, \(P_{\rm total}\), is based on the total number of moles of gas. And that number of total moles of gas is made up of at least two or more different gases that make up the mixture. So each individual gas imparts a partial pressure to the system. All those partial pressures will sum up to equal the total pressure.
Total Pressure of a system is always counting all the gas particles, no matter what kind they are. They all contribute to the overall pressure, \(P_{\rm total}\).
Partial Pressure of a system is always counting a specific type of gas particle which is called out. The partial pressure of gas A in a mixture of A, B, and C has nothing whatsoever to do with what B and C are or how much there is. Find the amount of A (atoms, molecules, or moles) and it will be directly used for \(P_{\rm A}\). The same holds true for gases B and C.