Short answer (Edited and expanded)
A full one would require a book or several.
Gothic architecture was a break from the Romanesque style which preceded it, based on round arches, fat columns, and thick walls or buttresses to bear the downward and outward thrust, and small windows. The pointed arch of the Gothic is more efficient at load-bearing; it also deals better with changes in space - eg a wide nave meeting a narrower transept - since the angle of the arch can be varied without awkward junctions.
This, together with flying buttresses enabled Gothic (churches) to rise higher, use slimmer, often clustered, columns and, crucially, permit more window openings. They were open to the Divine light, windows into Heaven.
1) Rheims Cathedral Interior
When the Renaissance rediscovered Classical Greco-Roman architecture, Gothic was seen as a debased style; the very term "Gothic", suggesting barbarous and uncivilised, was a term of abuse. The "Classical language" of Greco-Roman architecture was revived, influenced by people like Palladio. Classical architecture rejected the flamboyance of the Gothic for restraint, harmony and proportion.
2) Chiswick House, London
Finally we come to the Baroque! Baroque used the Classical forms, but in new and innovative ways. (The term "Baroque" originally meant a defective pearl, and came to mean "eccentric, bizarre".) Where Classical architecture is restrained, Baroque is monumental, tectonic: it handles space in a totally new way - colonnades sweep round, facades advance and retreat, mass is piled upon mass.
3) Blenheim Palace
4) Castle Howard Yorkshire England - Great Hall
If you compare the interior of Rheims Cathedral (1) with the Great Hall at Castle Howard (4) you will see how different they are. Yes, they are both lofty and enclose large spaces, but there the similarities end. Rheims is linear, leading the eye to the sanctuary and High Altar. Castle Howard is self-referential - it is saying "Look at me" (not God!) And the actual forms are completely at odds; the Great Hall uses round, Romanesque arches, but built on giant pillars, themselves resting on monumental plinths. The statuary is classical, Romans or psuedo-Romans, not saints or Biblical figures. Yet even these "heroic" figures are dwarfed by the scale of the setting, which is literally awe-inspiring.
Baroque became the architectural language of power - popular in Catholic, absolutist France, largely rejected in Protestant, constitutional Britain, where it was frequently laughed at. Pope famously remarked about Blenheim :-
Thanks, sir, cried I, tis very fine,
but where do you sleep or where d'ye dine?
I find by all you have been telling,
that 'tis a house but not a dwelling'
Pope arguably missed the point. The Baroque was no more about comfort than it was about religion. It was power and magnificence in stone.
Recommended : 50 Architecture Ideas you need to know Philip Wilkinson London 2010
(All illustrations from relevant Wikipedia pages.)
