As Cynthia rightly explained, "as" and "since" are subordinating conjunctions. This means they perform a function of providing a reason / explanation. They are used in subordinate clauses (which is the reason for the word "subordinating".
Examples of subordinating clauses are:
1. Since it had started snowing
2. ........... as they had already missed their flight.
Notice that they provide a reason but the clauses do not offer a complete and independent meaning. They are used with main clauses.
Since it had started snowing (subordinate clause with the subordinating conjunction "Since"), the runway was closed (main clause).
2. They took the train (main clause) as they had already missed their flight (subordinate clause with the subordinating conjunction "as")
The conjunction "as" can also be used to describe simultaneous events.
Example: As Mom was cooking dinner, the doorbell rang.
The conjunction "since" can also be used to describe the beginning of an event.
Example: It has been raining since morning.
I hope this helps.