OK, first off, what they were called back at the time of their use: "Sword", "Gambeson" or "aketon". - as simple as that. all the names are modern creations to differentiate between one and another. Taxonomical definition's very much a modern phenomena.
That said, this is the 21st C, so we all want our definitions.
the easy one first:
Gambesons and aketons/cotuns/juipon (all sort of interchangeable names) - Aketons are padded garments worn
underneath mail. Gambesons are padded garments worn
without mail. if its a garment worn underneath plate, its often called an Arming Doublet in historical texts.
For swords: its rather contextual on what date.
Longsword was a term that was used generally to describe one-handed blades of longer or narrower proportion,
or swords with a hand to hand and a half grip with similar blades, as time went on. Its sole identification, really, was that it was a longer style of sword, when compared to the shorter, earlier viking and norman age blades. But what was a long sword for 1200, was quite stubby for 1550's, so the definitions were always in a state of flux. Which is why those of us who have to deal with them on a daily basis prefer to use the Wheeler, Petersen, Gebig, Norman and Oakeshott Typologies (Particularly Oakeshott for medieval swords.), with terms like "Type XIIIa, 92cm blade, Type 2 cross, 25cm hilt, Type J pommel", rather than the vagueness of phrases like longsword/hand and a half/twohander, as it minimises confusion.
Hand and a half, as a generalisation, refers to those longswords which are balanced to be used either one-handed or with a second hand on the grip with equal ease. A lot of these swords have the scent-stopper pommels which are more comfortable to use with the hand on the pommel than the flat wheel pommels.
So, not all longswords are hand and half swords, but most
(there's always a few troublemakers that fall outside the norm) hand and a half swords are longswords.
Equally, almost all two-handed swords are longswords.
Bastard sword tends to be used nowadays to define later 16th Century complex-hilted longswords, such as this example:
Bastard Sword
they're intriguing ones to use (and a nightmare to make; all forgewelded bars and weird angles!), as they're designed and balanced to use one-handed, but with the capability to be held with the 2nd hand for the earlier longsword techniques. A number of them have survived which have had the knuckle-guard sawn away, often leaving marks on the forward guards, which clearly shows that the user(s) preferred to be able to use them with the 2-handed techniques from the Lichtenaur tradition, which meant being able to rotate the false and true edges on a few occasions.
as for what to call an albion Meyer....
well, i'd call it a Federschwert, given the construction of it with schilt, and rebated edge. Just to make it even more confusing!