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Please explain what is the difference between TableBox, TabularSection and ValuesTable?
Why when I drag a TabularSection on a form I can not do most things with it when accessing as Items.MyTabularSection which I can do with it when access it as Object.MyTabularSection?
And why I can not get the CurrentRow from Object.MyTabularSection while I can get it from Items.MyTabularSection?

ValuesTable - the object that allows you to build a dynamic set of values ​​and manipulate (add, edit, delete entries, sort). Can be filled with the values ​​of any type, ie in one table types stored values ​​may be different. The object of this type are not sohranyaetsyav database.
>Please explain what is the difference between TableBox, TabularSection and ValuesTable?
TabularSection - part of a document, manual, etc. Is not an independent object but only its part. All objects contain a TabularSection stored in the database.
Tablebox-control that enables you to work with a variety of lists, sets of records, as well as dynamic data sets and ValuesTable ValueTree.
Type a string value tablebox field depends on the type associated with the tabulated values ​​of the field.
That is, is a visual representation of some data that migut be ValuesTable and TabularSection.

>Why when I drag a TabularSection on a form I can not do most things with it when accessing as Items.MyTabularSection which I can do with it when access it as Object.MyTabularSection?

Cause doing the drop on the form of drops is not a TabularSection Tableboh (connected with the original tabularsetstion (property DataPath)). And this is another type of object, and it has different properties and methods.

>And why I can not get the CurrentRow from Object.MyTabularSection while I can get it from Items.MyTabularSection?

As he wrote - it's different objects with different methods and properties.
In TabularSection no current row, it is a visual element forms TableBox.
If you want to get the line number corresponding TabularSection CurrentRow element tablebox, you can use the following code:
IndexCurrentRow = TabularSection.IndexOf(FormItems.TableBox.CurrentRow);

This returns a numeric value between 0 (if corresponding first row, there have not worked a rule: 1 = index number of the line). In the case of an unsuccessful search will be returned as the result of -1.

I apologize for my English.

Thank you very much, Escander for the explanation!
Some words I couldn't get: sohranyaetsyav, migut, but the most things I understand now. If I'm right,

ValueTable is a separate table in operating memory
TabularSection is a table connected to the Object and is stored in the infobase
TableBox is a table representation on the form which can be changed with user actions

So because of the TableBox is the only table of those 3 which is displayed on the form it can have the current row. While others are not accessible directly by a user and can not be clicked on a row and have it selected to have a current one.

Am I correct?

ValuesTable - Data type(like array, numeric, boolean)
TableBox - Visual control wich can be placed on the form, in fact using for data(valuetables) input.
TabularSection - Visual control for data representation for sending to the printer(for example).
Sorry for my bad English.

Oh no.. TabularSection it's part of Document or Catalog, wich can be represent on the Form with TableBox control.