This rule appears in Chapter 9: Spellcasting of the Basic Rules (and PHB). In the Casting Time section, it states:
A spell cast with a bonus action is especially swift. You must use a bonus action on your turn to cast the spell, provided that you haven't already taken a bonus action this turn. You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action.
In the same chapter, under Cantrips, the rules define a cantrip as:
a spell that can be cast at will, without using a spell slot and without being prepared in advance.
(Emphasis mine in both excerpts.)
When the rules specifically exclude cantrips, they use the phrase “spells of 1st level and higher” (for example in the Spellcasting class features granted to many classes). The term “spell” on its own includes both cantrips and higher level spells.
Therefore yes: if you use your Bonus Action to cast any spell with a casting time of 1 Bonus Action, including the cantrips magic stone and shillelagh, you can then use your Action in the same turn to cast a cantrip with a casting time of 1 Action.