Distinct, separate, several, discrete are comparable when used in reference to two or more things (sometimes persons) and in the sense of not being individually the same.
Distinct always implies a capacity for being distinguished by the eye or by the mind as apart from the other or others, sometimes in space or in time but more often in character, nature, or identity.
Separate (see also SINGLE) is often used interchangeably with distinct and often in combination with it, as if one strengthened the other.
But separate stresses, as distinct does not, the lack of a connection between the things considered, usually by reason of the distance in space or time or the difference in identity of the things in question; thus, a drama with two separate plots is not the same as one with two distinct plots, for separate implies no connection (or, often, only a factitious connection) between the plots, while distinct suggests only that they can be distinguished.
Separate is also often used in preference to distinct when an opposition to common or shared is implied.
Several (see also MANY) is somewhat formal or old-fashioned in this sense; it implies an existence, a character, a status, or a location separate or distinct from that of similar items.
It may modify a singular noun, especially when “each” precedes, as well as a plural noun.
Discrete, even more than separate, implies that the individuals are not the same and are not connected; it is often more precise than separate because it stresses numerical distinctness (that is, distinctness as individuals) rather than difference in kind, nature, or goal; thus, discrete things may be exactly the same in appearance, nature, or value, but they are not selfsame and are physically disconnected.