You already answered your first question, so I'll answer the second: "Is it the same now?" The question is vaguely worded, so I'm going to assume that you mean, "Is the command in force for today?" The passage you chose seems to indicate that it should be the same now.
Wherefore the children of Israel shall keep the sabbath, to observe
the sabbath throughout their generations, for a perpetual covenant. It
is a sign between me and the children of Israel for ever: for in six
days the LORD made heaven and earth, and on the seventh day he
rested., and was refreshed.
Every sabbath he shall set it in order before the LORD continually,
being taken from the children of Israel by an everlasting covenant.
It shall be a sabbath of rest unto you, and ye shall afflict your
souls, by a statute for ever.
And it shall come to pass, that from one new moon to another, and from
one sabbath to another, shall all flesh come to worship before me,
saith the LORD.
These passages clearly indicate that God did not intend for the sabbath to stop. He expected His people to keep them “perpetually,” “a statute for ever,” “from one new moon to another,” “throughout their generations.” How many different ways does He have to say it before we get the point – the sabbath was meant to be kept always?
Clearly, the sabbath statutes are not supposed to end. But is that the real meaning of “perpetual”? Let’s take a look at other verses using this word and let the Word interpret itself:
And thou shalt gird them with girdles, Aaron and his sons, and put the
bonnets on them: and the priest’s office shall be theirs for a
perpetual statute: and thou shalt consecrate Aaron and his sons.
We know from Hebrews 7:11-12 that Aaron’s office has been shut down:
If therefore perfection were by the Levitical priesthood, (for under
it the people received the law,) what further need was there that
another priest should rise after the order of Melchisedec, and not be
called after the order of Aaron? For the priesthood being changed,
there is made of necessity a change also of the law.
The Old Testament priesthood was not “perpetual” at all in the English sense of the word. The Aaronic priesthood (with the Levitical priesthood) came to an end when Jesus came. When Jesus came, the law changed. So the law was never meant to continue forever. “Perpetual” means a long time, not forever.
Look at a couple more instances of “perpetual.” God speaks of perpetual judgment on Israel:
To make their [Israel's] land desolate, and a perpetual hissing; every
one that passeth thereby shall be astonished, and wag his head.
And I will bring an everlasting reproach upon you, and a perpetual
shame, which shall not be forgotten.
Has this judgment continued on Israel? No, for God has shown mercy and Israel has prospered abundantly. The perpetual was conditional. Perpetual does not mean forever, but a long time, until something else interrupts it. In this case, Jesus’ priesthood replaced the Levitical priesthood, as mentioned previously. Why is this significant? Because the Levitical priests officiated over the sabbath. If there are no Levitical priests, the sabbath cannot be observed.
"Is it the same now?" No; the sabbath is not to be observed in the same way as in the OT. You mentioned Matthew 12:8, in which Jesus said that He was the Lord of the sabbath. That saying was prompted because Jesus broke the sabbath law!
It was against the sabbath law to work. Plucking ears of corn was considered work, not rest. Yet Jesus, the Author of the sabbath, had no problem with His disciples helping themselves to the corn. What was the guiding principle here? Mercy and compassion should guide the application of any spiritual law. The disciples were hungry, so they should eat, sabbath or no. When Jesus said that the sabbath was made for man, He was saying that the sabbath yielded to the needs of man. Furthermore, the Son of Man is Lord of the sabbath. The sabbath was not the highest law. Jesus is even higher than the sabbath. This means that following Jesus is a higher priority.