The word is slightly misleading: nothing is pushed out across the internet. Your authoritative nameservers serve the new record immediately. What takes time is that recursive resolvers around the world each hold a cached copy of the old answer and keep using it until its TTL runs out. Every resolver cached it at a different moment, so they switch over at different moments.
The upper bound is therefore the TTL the old record had, not a fixed "24 to 48 hours". A record with a 300-second TTL is replaced in resolver caches within about five minutes. Nameserver (NS) changes are slower because the delegation in the TLD zone typically has a TTL of a day or two. Negative answers are cached as well, for the time set in the SOA record.
A propagation check asks the same question of several public resolvers and compares the answers. It can show that a sample of resolvers agree; it cannot prove that every resolver in the world has the new value, which is why OrbitProbe reports results as "N of M resolvers" and nothing stronger. Browsers and operating systems add their own caches on top.