SQLite wildcards in Join

In a previous question of mine it appears as though my problem is SQLite dependent. I have simplified the problem as follows:

Say I have two tables: table1 as follows

Name     | col1
------------------------
 Bob     | B1
Mary Jane| M1

and table2 as follows:

Name     | col2
------------------------------
 Bob     | B2
Mary     | M2

What I would like is to JOIN these together to obtain:

NameA     | NameB |col1| col2
-------------------------------------
 Bob      | Bob   | B1 | B2
Mary Jane | Mary  | M1 | M2

Using

SELECT tablea.Name as NameA, tableb.Name as NameB, tablea.col1, tableb.col2
FROM table1 as tablea
LEFT JOIN table2 as tableb
ON tablea.Name LIKE tableb.Name

I get as output

      NameA NameB col1 col2
1       Bob   Bob  B1   B2
2 Mary Jane  <NA>  M1  <NA>

which is what I would expect. Now if I use wildcards as follows:

SELECT tablea.Name as NameA, tableb.Name as NameB, tablea.col1, tableb.col2
FROM table1 as tablea
LEFT JOIN table2 as tableb
ON tablea.Name LIKE '%'+tableb.Name+'%'

I get:

      NameA NameB col1 col2
1       Bob  <NA>  B1  <NA>
2 Mary Jane  <NA>  M1  <NA>

It doesn't even match Bob's entries?!

Am I missing something? Is this a problem with SQLite?

For completeness, I'm using the sqldf function with R which uses SQLite.