Answer Description

Based on the description given this is most likely port scanning to determine which ports are open and listening for TCP connections. Specifically this is called SYN Scanning, which is a type of port scanning.

A SYN flood, Distributed Denial of Service (DDoS) and DoS attack would likely be hitting a single port or only a few ports with a large amount of traffic to overwhelm the service. While a port scanner will hit many or all ports with only 1 or a few packets per port.

Wikipedia

A port scanner is an application designed to probe a server or host for open ports. Such an application may be used by administrators to verify security policies of their networks and by attackers to identify network services running on a host and exploit vulnerabilities. A port scan or portscan is a process that sends client requests to a range of server port addresses on a host, with the goal of finding an active port; this is not a nefarious process in and of itself. The majority of uses of a port scan are not attacks, but rather simple probes to determine services available on a remote machine. To portsweep is to scan multiple hosts for a specific listening port. The latter is typically used to search for a specific service, for example, an SQL-based computer worm may portsweep looking for hosts listening on TCP port 1433.