Good question! Thank you!

The short answer is that logical positivism was always extremely diverse, and there's no reason to think that there's a consistent core to it, but if there is then it has to do with a belief in making progress in philosophy and science by (a) using logic to build on (supposedly) certain foundations (although they didn't agree on what those foundations were), and (b) repudiating metaphysics (which meant different things to different people, but which IMO was probably the most important point of agreement among the logical positivists anyway).

They were all influenced by Bertrand Russell's earlier claim that philosophy should proceed by using logical arguments based on certain premises (to the extent possible - he didn't think it was always possible), and that it should define terms strictly, based on what was already known, as opposed to positing anything. They were also all (I think all - certainly most of them) influenced by Einstein's ideas. Neither Russell nor Einstein was verificationist.

Verificationism was fairly popular among logical positivists, especially at the beginning, and especially in English-speaking countries, because Ayer, who was not one of the founders of logical positivism but who visited Vienna while he was a student and wrote an early and very popular book about it in English, stressed verificationism. But Ayer's book was over-simplified in its presentation of what logical positivsm was (IMO), and in any case logical positivism continued to develop, with almost all of its important literature being in German.

All the major logical positivists (I think - certainly most of them) sooner or later - and in some cases very soon - gave up on verificationism, but still called themselves logical positivists (or logical empiricists, which was and is usually thought to be more or less synonymous).

From the 1930s onwards, English became more important than German for the first time, and the most important logical positivists were then those who were in English-speaking countries, especially Carnap in America (and arguably Wittgenstein, depending on whether you think he'd been a logical positivist to start with). All of them (I think, and certainly Carnap) repudiated verificationism pretty early on, athough Carnap continued to call himself a verificationist in some contexts, while the rules he proposed were much more complicated than the original verificationism (I wouldn't call them verificationist at all, just anti-metaphysical ... but admittedly this is controversial).

All that time, logical positivists were working on many systems of philosophy and science that used logical principles to construct claims about the world from supposedly certain foundations plus strict definitions, eschewing metaphysics. That was what they saw their job to be.

Someone COULD argue that verificationism was always something logical positivists felt they had to try to stick to to some extent (although IMO even that would probably be an over-simplification). But to say that logical positivism and verificationism were the same thing is totally wrong, historically. More specifically, criticising logical positivism by only criticising verificationism doesn't hit the target. Criticising it by criticising logical constructions might work, or, as became popular in the very late 20th century, you could criticise it by saying that it was wrong to repudiate metaphysics. Those two criticisms would at least be on target, whether or not they work.

It's all super interesting and I encourage you to read https://plato.stanford.edu/entries/logical-empiricism/ :-)