The butcher in Pharaoh's "jail"

Question

In Bereshis 39:20 Joseph's master puts him in jail, there termed בית הסהר. In chapter 40 we have (v3,4)

וַיִּתֵּן אֹתָם בְּמִשְׁמַר, בֵּית שַׂר הַטַּבָּחִים--אֶל-בֵּית הַסֹּהַר: מְקוֹם, אֲשֶׁר יוֹסֵף אָסוּר שָׁם וַיִּפְקֹד שַׂר הַטַּבָּחִים אֶת-יוֹסֵף, אִתָּם--וַיְשָׁרֶת אֹתָם; וַיִּהְיוּ יָמִים, בְּמִשְׁמָר

There are a few things I don't understand about this

1. what is the difference, if any between בית הסהר and מִשְׁמָר
2. Why is the head butcher in charge of the jail?
3. Isn't the head butcher Potiphar (37:36)? If so why would he put Yosef in charge of the jail if he just jailed Yosef for abusing the privilege of being in charge of his home?

Answer 1

See Ibn Ezra on Breishit 40:4. I'm summarizing what he states:

שַׂר הַטַּבָּחִים had the jail in his house, and placed Joseph there in charge of the other two people because he remembered the good job that Joesph did watching over his own home. (Combine this with what was said in @DoubleAA's comment above - he doubted that what his wife said was true.)

Ibn Ezra seems to say (I'm not totally sure but my best understanding) that בית הסהר and מִשְׁמָר are synonymous within this context.

However, the term מִשְׁמָר means "under observance", and doesn't necessarily refer to the name of a physical place. סהר is an unusual word, which does not seem to havea Hebrew counterpart, and these are the only places in Tana"ch where this term is used. Ibn Ezra on verse 21, says, specifically that since it doesn't appear to be Lashon Hakodesh, the Torah explicitly describes what it is by stating "the place where the king's prisoners are imprisoned". So, in short, בית הסהר means "prison".

As for question #2, see @Shalom's answer to this question, asked yesterday. According to Ramban, שַׂר הַטַּבָּחִים was the chief executioner. If so, it makes sense that he is in charge of the jail!