This is a great question, but the terms you used are a bit anachronic in the frames of Pre-Roman Europe, or at least deserve to be pruned a bit.

Western Europe before Roman conquest is dominated by La Tène archeological culture, a vast ensemble of related material culture which at its apogee covered a significant part of Europe, from southern England to Northern Italy, and Spain to Ukraine. Latenian material culture is generally associated with mainland Celtic peoples, which are tought to have lived in the area since at least the late Bronze Age within the frames of Urnfield culture or complex where geographical and material overlapping with the next material culture known as Halstatt culture.

By the Ist century BCE, Latenian material culture was distinctive of peoples known as Gauls (outside Gaul in the strictest sense, and found as far as Ukraine and Anatolia) and Brittons.
We should be careful, now, not to systematically equate Halstatt or La Tène with Celtic peoples : northern Britain and Ireland, while inhabited by Celtic-speaking population in the Iron Age, weren't really part of these cultures altough they recieved some influence and obtained products from their neighbours. On the other ends of these material cultures, especially in Germania, and areas now in modern Poland, Yugoslavia, Rumania and Ukraine; it is highly suspected that La Tenian culture wasn't exclusively Celtic-speaking (while, carrying a lot of traits associated with Celts) but a mix with Germanic, Iranic and Thracian elements.

"Celtic", indeed, is more of an historiographical term for what could be best described as a "meta-civilization", common traits and principes found in a variety of autonomous cultures and contexts. There's no real evidence that Celtic peoples ever felt they shared a common identity or relation as a whole. It came into being partly because Greeks, and later Romans, used systematisation and standardisation to understand the hinterland of a whole set of Barbarian situations they only knew trough coastal control : it's quite possible that Keltoi was first the name of a confederation in southern Gaul (with cognates in Iberian peninsula : Keltoi might have been a fairly prestigious and common name to be claimed;not only Goth in Late Antiquity) whom usage was sytematized both by Greeks to name the whole population in the North that could be or not be related to southern Gaulish peoples; but as well was sytematized by Gauls themselves as the rough confederation came to encompass most of Gaul (hence "Celtic Gaul" identified apart from related Germania's peoples)

Eventually, in western Europe, we can identify rough cultural ensembles (which were really porous to each other) before the Roman conquest.

Gaulish culture in Gaul, obviously, but as well in southern Germany, in Northern Italy (where Lepontic culture might have been a different archaic branch in the Vth century, or conversely an archaic Gaulish situation), alongside the Danube in conjonction with Thraco-Dacian peoples and in Anatolia. Their names is an evolution of Latin Galli, which might be a transliteration of the greek Galatai, itself a possible transliteration of gaulish Galatoi, whom origin is murky at best but might comes from a different coalition name in Gaul which fell into disuse among Gauls themselves who adopted Keltoi as their endonym.
Gaulish culture was unmistakably Celtic linguistically (what we know of their language leaves no doubt) and is one of the best known Celtic cultures of the Iron Age, thanks to Greek and Romans who traded and fought with them since the Vth century BCE and let few but important accounts about them, but as well a booming archeological understanding of their history since the 1970's.
But as they are the best documented ancient Celts, a lot of features of their culture was often systematized to the whole meta-Celtic ensemble : while Druidism is attested only in Gaulish and British culture, it was sometimes made pan-Celtic feature.

These Gauls weren't necessarily a culturally unified people (altough there's no real reason to think they didn't shared a same language, at the exception of Aquitain Gaul) and under Druidic influence, a territorial Gaul came to differenciate and define itself within limits smaller than Gaulish culture in the broad sense : roughly, Pyrenees to Rhine and Alps.
Relation with Brittons or Celts of Germania was acknowledged (it's possible that Germani is the translation of a term meaning roughly "Relatives"), but what eventually set apart from Gaul as a political and cultural concept, dominated by Keltoi, but incuding differenciated ensemble from the IIIrd century BC onwards such as Belgians ("the furious ones"?), a Germanic (but Gaulish-speaking and definitely Celtic) group that took over the region between Rhine and Seine trough fight (evidence of large battles in Gaul can be found in this period, such as in Ribemont) but as well patronage and alliances with native. Another sub-ensemble in Gaul could be Aremoricans ("those close to the sea"), which Romans had trouble really differenciating from either Celts (in the sense of Celtic Gaul, not pan-Celtic) and Belgians, whom distinctiveness might come from a common origin (peoples displaced by Belgians according Poseidonios and Strabon) and regional military and commercial alliances (notable in trade with Britain).

Gaulish political organisation was set on regional or pan-Gaulish councils tought to have pre-existed Romans. These assemblies were based on common ancestry (real or percieved) and ancient ties, roughly fitting the aformentioned ensembles : Celts, Belgians, possibly Aremoricans in addition of a pan-Gaulish council ("the assembly of the whole Gaul" described by Caesar) as well as druidic assemblies. In these frames, where patron peoples were chosen (for Celts, possibly Bitouriges, then certainly Areuernoi and Aidu(s)oi in historical times; for Belgians Remi, for Aremoricans maybe Uenetoi) existed as well broad confederacies (regional patrons being favoured there, but other confederal patrons could emerge) of peoples with at least a mention of a real federation (between Remi and Suessiones).

Now, when saying Belgians came from Germania, it should be understood as coming from the Germanic area and not culturally/linguistically Germanic. The advence of proper Germanic peoples was a later occurence within Germania itself roughly from the IInd century onwards and a lot of peoples and coalition in Caesarian period had Celtic features, names more or less importantly mixed with Germanic traits. For instance, Ariouistos (Ariovist) while leader of a Germanic league had a Celtic names and ruled over peoples with Celtic names as well as Germans. The differenc existed but was exacerbated by the decline of Gallic people (partly due to the Roman conquest of Gaul) and the differenciation between Roman Gaul and Barbarian Germania which represented the first radical rupture on the Rhine.

Knowledge about "Celto-Germans" such as Boioi, Touriscoi living along the Rhine and Danube is limited, having been less of a focus for ancient scholars than Gaul itself, but historical and archeological records doesn't really mark a significant difference with Gaul's Gauls in language or material culture. They formed regional confederations, traded with Romans (and as in Gaul, were partly romanized before the conquest). They seem however to have suffered significantly from the Cimbric war more than Gaul itself, as well from the brutal Roman conquest of Gaul (the oppidum of Manching declined and collapsed before the Roman conquest of its region)