Parallelism studies systems that contain several parts where computations happen at the same time. Let's call these parts nodes. If all the nodes are deterministic (e.g. no random generator) and they all execute instructions at the same speed (i.e. they all have the same clock), then the system as a whole is deterministic: the state at time $t+1$ is fully determined by the behavior of the system at time $t$ and the way each node executes instructions.
An example of a parallel system is a microprocessor or microcontroller. All but the most basic processors have multiple subsystems that execute in parallel. Each instruction moves through the stages of a pipeline, and at any given time, the processor is in the process of executing many successive instructions, potentially one at each stage of the pipeline. It is essential for the design of the processor to know exactly when the data for an instruction will reach each component, and how much time (how many clock cycles) it takes to go from one component to the next.
Hard real time systems are also deterministic, and often parallel. For example, the controls of a vehicle consist of many processors, and the critical parts (engine, brakes — not e.g. the entertainment system) operate at a known speed with known reaction times. There is a class of programming languages, synchronous programming languages, designed to program such systems, which model parallel execution in a fully deterministic framework.
There are also higher-level parallel systems which are deterministic even though the lower-level layer isn't. This is typically the case when doing numerical processing. When a computation can be parallelized, the parts are dispatched to different processors, and the exact time they take to process their parts can depend on how fast each node is, how much communication bandwidth is available between the various nodes, on how the data is arranged, etc. The duration of the computation is not deterministic, but the result is: it's equivalent to running all the computations sequentially on a single processor. The reason such computations can be parallelized is that they contain parts that don't depend on each other, so it doesn't matter in what order these parts are executed — or whether some are executed at the same time on different nodes.
Terminology isn't completely standardized, but generally parallelism is used when systems are deterministic (at least as far as the result of the computation is concerned), and concurrency when systems are not deterministic. Concurrency studies systems where events can occur at unpredictable times, such as user input, network reception, etc. See also Distributed vs parallel computing