Checking through Joe Biden’s Wikipedia page for obvious reasons I found a table that seems to say that he switches between the Republican and Democratic party after each senate term.
No, you aren’t. Everything shaded in red applies to his opponent in the year indicated in the first column: name, party, votes, percentage. I presume that “party” is listed there because there is an (unlikely) chance that his principal opponent might not be a Republican.
The different colours in the table headed “United States Senate service” are the party majorities in the US Senate, not the party allegiance of Senator Biden.
You were probably looking at the graph entitled “United States Senate Service”
In the US we label our Congresses in a similar manner to the way you name “Parliments” in the UK. We are currently on the 110th Congress. Since every Representative in the House is re-elected every two years, it makes sense to divide them up into two-year chunks.
Now for Senators, I guess they also go by the same time chunks as the House, meaning that each Senator would serve for at least 3 Congresses. Senators server 6 years. In any case, the reason why it flips from red to blue is because that represents which party had the majority during that Congress.
He didn’t really gamble on it; didn’t he lose in the Democratic primary, then run as an independent? Also, it’s worth noting that he calls himself an Independent Democrat and caucases with the Democrats.
Also worth noting that politicians are much less tied to parties in the US than in the UK. Switching allegiances outright is rare, but it’s not rare at all to vote with the other party. It happens in virtually every vote in the states, but virtually never in many parliamentary states.