Not at all, ping is just a nickname for an ICMP echo message and the name of the /usr/bin/ping program.

The output of the program are RTT minimum, max, average, mean deviation and percentage of packet loss.

You can also measure latency over UDP and TCP using other tools. For 99% of practical use cases there is actually no meaningful difference.

Can you explain to me why and how this can be different?

Your provider can for example filter out all ICMP packets giving you timeouts for "ping", but you can still reach the host just fine with other protocols. Similarly your provider probably prioritizes protocols that require low latency like VoIP over ICMP packets.

Alternatively, they might prioritize small packets and ping will be misleadingly fast compared to bigger data flows.

Another possibility too is that your pings don't experience any packet losses, whereas actual data does which would increase the real latency.

In short, there are many potential differences between ping and actual latency.