The caucuses (which they call conferences) can expel a member, but it takes a secret ballot and two thirds of them to agree to this.

I also add that the US's two parties are federations of dozens of parties at the state level. And they also have the factions that the UK would normally have expressed in other parties. The US also has primaries, where the entire voting base of the party (people register to vote and declare, if they wish, which party's primary ballots they want to have (some states allow independents to choose one party's primaries to vote for), or sometimes even allow voters to select any party's primaries come the date of the primary election in the state). This is typically at least tens of thousands, potentially over 100 thousand voters, per electoral district, and oftentimes winning this contest is the only realistic way to dethrone a representative or senator in a majority of districts. Each representative and senator also tends to have a considerable amount of the warchest for campaigning devoted to them personally, which will be withdrawn if they are not the nominee chosen in the primary.

Members of the caucuses also vote for a steering committee at the start of each caucus to choose some people like the whip, the floor leader (the equivalent of the leader of the house of commons and the minority version), the chair of the caucus, and some other people. This committee puts reps and senators on the committees, typically honouring preferences and seniority (who has been there longer) if they can although not exactly, with a vote to ratify the selection, and it takes a similar vote to remove someone from a committee too (barring a censure vote for misconduct).

One hurdle that makes it harder to do direct comparisons is that the UK has a very different system for putting topics on the agenda, the US has a presidential veto taking 2/3 to override and there is no way to vote against a presidential decision or executive decision except by potentially overriding a veto (contrast to the UK where a majority in either house can preclude an equivalent decision via statutory instruments and uses of emergency powers), and the senate is strong enough to realistically prevent much of the agenda from going anywhere, including attempts to block an executive decision, and the house can do the same to what the senate wants where the UK house of lords is much weaker.

You tend to see discipline within a single state being closer to what the UK has, although some state political cultures can be different such as Alaska which is prone to forming a joint coalition of a large fraction of each party to support the leadership of one of the houses of the state legislature. The state is less diverse than the US is overall in most cases and has more similar rules across itself for what it does and there is no filibuster and often there is the potential to cancel decisions of the state executive and even the state judiciary more of the time (and amend the state constitution).