Do Jews keep the mitzvot the same way?

Answer 1

The same way as each other:

Yes, with some exceptions, such as Reform Jews praying in English, or keeping one day Rosh Hashanah instead of two. Otherwise, those who ignore the mitzvot just don't keep them (or most of them) at all.

The same as in the past:

Judaism centers around Torah-observance. This has never changed. The Torah contains many hundreds of commands, and we keep whichever we can, as hundreds of them are applicable today too. When the Temple was destroyed, certain commands of the Torah were suspended, but did not change. It's like a man who lost his arms: he doesn't put tefillin on, but his Judaism hasn't changed. - While the Torah, its commands and the principles and beliefs of Judaism remain unchanged, Judaism has evolved as circumstances have necessitated. There are many Rabbinical decrees, mostly from the Men of the Great Assembly (4th century BCE), as well as later enactments.

The purpose of every one of them is to provide a "fence around the Torah," meaning to shore up something that can benefit from strengthening, without changing the relevant Torah-command. An example: not handling electric appliances on the Sabbath, even if they are not connected to any electric socket.

Answer 2

The same way as each other:Yes, with some exceptions, such as Reform Jews praying in English, or keeping one day Rosh Hashanah instead of two. Otherwise, those who ignore the mitzvot just don't keep them (or most of them) at all.

• Link: How do the Orthodox differ
  

The same as in the past:

Judaism centers around Torah-observance. This has never changed. The Torah contains many hundreds of commands, and we keep whichever we can, as hundreds of them are applicable today too. When the Temple was destroyed, certain commands of the Torah were suspended, but did not change. It's like a man who lost his arms: he doesn't put tefillin on, but his Judaism hasn't changed.
While the Torah, its commands and the principles and beliefs of Judaism remain unchanged, Judaism has evolved as circumstances have necessitated.
1) After the end of prophecy (some 2350 years ago), the Hebrew Bible was sealed by a special Sanhedrin (Rabbinical court). It was the same Sanhedrin which placed our prayers in their permanent form (Talmud, Berakhot 33a).
2) Purim and Hanukkah were instituted after the relevant events.
3) Certain fasts were instituted in connection with the Destruction of the Temple.
4) After the Destruction, the laws of sacrifices were suspended.
5) When circumstances made it impossible, the New Moon was no longer proclaimed by testimony; rather, the fixed calendar was instituted (around 360 CE).
6) The Talmud was put in writing (around 500 CE) when it became too hard to be learned by heart.
7) There are seven formal Rabbinical commands. These are:
Saying the blessings over food (and on various occasions)
Washing one's hands before eating bread
Lighting the Hanukkah-menorah
The Eruv
Saying the Hallel prayer on certain occasions
Lighting the Sabbath candles
Reading the Megillat Esther on Purim.
In addition, there are many Rabbinical decrees, mostly from the Men of the Great Assembly (4th century BCE), as well as later enactments.
The purpose of every one of these is to provide a "fence around the Torah," meaning to shore up something that can benefit from strengthening, without changing the relevant Torah-command. An example: not handling electric appliances on the Sabbath, even if they are not connected to any electric socket.

See also the other Related Link.

Link: Was Judaism altered after the destruction of the Temple?