The only distinction is that Orthodox Jews and Orthodox Christians disagree on which individuals should be venerated.
If a Christian is an idolater for visiting Lourdes, a Jew is an idolater for visting the grave of the Baal Shem Tov.
Now widey, you know better than that. There is simply no comparison between Jewish veneration of the Sages and the chrstian "cultus" of the "saints." There are no formal, official prayers to the Sages nor are "icons" or statues of the Sages prayed before. No one has a "patron sage" nor are their "feast days" for them.
Any glance at a Siddur will show an unbridgeable gulf between Jewish and chrstian prayers.
As you know, ZC, Christians do not pray "to" saints, but ask saints to pray for them. Their names are invoked. And in the pious songs and prayers of Judaism, the prophets and sages are invoked as well.
or statues of the Sages prayed before.
Since Judaism eschews statuary, graves are typically used instead as special, physical places for the commemoration and veneration of the sages.
No one has a "patron sage"
Every community has "patron sages", usually the deceased rebbes of their community or the sages whose books are revered as valuable commentary in their communities.
nor are their "feast days" for them.
That would be news to the Ukrainian communities who are inundated with devout Hasidic pilgrims who come to venerate their sages on special days.
Any glance at a Siddur will show an unbridgeable gulf between Jewish and chrstian prayers.
A glance might create the impression of an unbridgeable gulf. An informed perusal would notice that a Siddur and a Christian Missal/Liturgy have very similar structures.
The core service opens with invocations, then blessings, then a doxology. There are readings from Scripture, there is often a homily, and a sequence. The most signal difference in the structure is that the Siddur has no sacrifice, while many Christian services do.
The similarities between the two stand to reason: the first generation of Christian worship often consisted of communal prayer in the synagogue followed by a sacrificial ritual in another location.
"Our Father..." sure seems like a Hebrew prayer to me.