French way of grouping French verbs
In France, verbs are categorised into three main groups based on the patterns in the way they conjugate. However, the third group is rather difficult to work with for non-natives and is taught differently outside of France.
Group 1 - Regular -ER verbs
All verbs ending in -ER (like aimer, parler, habiter), plus semi-regular verb groups (like -CER and -E*ER).
ATTENTION:
aller is the only -ER verb belonging to the 3rd group, because it's highly irregular!
Group 2 - Regular -IR verbs
All verbs that conjugate like finir, choisir, réussir.
Group 3 - All Irregular and Semi-regular verbs
The third group contains everything else: aller, irregular -IR verbs (like partir, sortir, dormir), -OIR verbs and all -RE verbs.
In total, between regular, semi-regular and irregular, there are 82 different conjugation patterns in French!
English way of grouping French verbs
There are several different systems used, but generally groups 1 and 2 are the same as in France (regular -ER and regular -IR verbs, though stem-changing verbs are adressed separately).
Group 3 -RE verbs
Since there's no general pattern to -re verbs, this is often taught as seven subgroups, including what we call regular -dre verbs.
Group 4 -OIR verbs
Three subgroups of some "irregular -ir verbs" including voir, savoir, recevoir etc. These are not consider "-ir verbs" in France because the sound of -oir in voir is very different to the -ir in finir. The conjugation patterns are about sound more than spelling.
Group 5 - Completely irregular verbs
Aller, être, faire, etc.