Proto Indo European is the grandfather or great grandfather of English (depending on how you count). This means that we can trace elements of Modern English all the way back to Proto Indo European which was spoken about 4000 BC.
Proto Indo European, like any language, had its own peculiarities. One of them was the “s-mobile” which refers to how the letter “s” sometimes just didn’t stay there in some words but did in others.
The s-mobile is indicated by a bracket around the letter s in words that have been reconstructed in Proto Indo European. We have to reconstruct them because no one wrote Proto Indo European down. We reconstruct words by looking at Modern Indo European languages like English, German, Spanish, Italian, Persian and Hindi and start finding connections between them.
English, German, Dutch, Danish, Swedish, Norwegian, Icelandic and a few others are part of the Germanic group of languages. They all descend from a language linguists call Proto Germanic.
If we don’t have direct evidence that a word existed then we say the word is reconstructed and we apply a star at the beginning. If a document exists that has the word in question in it, we say the word is attested.
The word for “bull” in Proto Indo European is *(s)táwros. Here we can see the star and the brackets. We know that the s was mobile because it appears in some descendant languages but not others.
The word *(s)táwros became “steer” in English, and “Stier” in German, but in Greek, the “s” wasn’t inherited, so we get “tauros”.
So what does this all have to do with spring and frog? Well, they are actually related because they both come from a Proto Indo European word with an s-mobile in it.
One last thing we need to know about to make sense of this. When Proto Indo European developed into Proto Germanic in Scandanavia, the sound “p” became “f”. But this did not affect other descendants of Proto Indo European. So for instance, it is “father” in English but “pater” in Latin.
But here is where things get weird (if s-mobile wasn’t weird enough already!). The sound change (also called a sound shift) of “p” becoming an “f” did not affect words that had the combination “sp”.
So in the Proto Indo European word *(s)preu (which means jump), when the “s” was present, the “p” stayed and turned into the word “spring”, but when the “s” wasn’t present, the “p” became a “f” and the word developed into the word “frog”. So “spring” and “frog” are what linguists called cognate which means they descend from the same source.
And now you can tell people that the frog is named after the fact that it jumps