Losing something and having something break are two VERY different things.
Actually, not in this case.
I mean that the way you lose your shield in OoT creates the vibe and feeling that your shield just got broken, cause, you know, it got EATEN! Also, when your shield gets eaten by a Like Like, you have to defeat it quickly to get your shield back, otherwise, it's gone, as in EATEN, CHEWED UP, DEVOURED, and most notably, BROKEN! Literally, if you waste time dancing with the Like Like, your Hylian Shield will be completely devoured and DESTROYED! In other words, BROKEN! Why do you think, after a certain amount of time dances with a Like Like that took your shield, after defeating it, your shield isn't there? That's because it's GONE! And by that I mean COMPLETELY BROKEN, CHEWED UP, and DEVOURED!
So, no, in this case and sense, it IS actually the SAME thing! Also, in a very old alpha version of OoT, the Hylian Shield was originally supposed to break in battle from taking hits. This was later replaced with Like Likes eating the shield. So, either way, the Hylian Shield was clearly NOT intended to be indestructible in OoT. This is mainly because of the Mirror Shield, which was the indestructible shield in the game.
Also, if the Hylian Shield were indestructible in OoT, the Like Likes would NEVER be able to EAT or DEVOUR it! And you would NOT lose your shield at all! You would keep the shield no matter what. That said, in order for Link's shield to be eaten up by Like Likes, it HAS to be able to BREAK! In other words, my point stands tall.