Even though you have different partition functions you can swap the partition out because the structure is the same and the partition boundary in the source is a subset of the boundary in the destination. Running this query (credit to Dan Guzman) we can see the boundaries of each partition:

--paritioned table and index details

SELECT OBJECT_NAME(p.object_id) AS ObjectName,

i.name AS IndexName,

p.index_id AS IndexID,

ds.name AS PartitionScheme,

p.partition_number AS PartitionNumber,

fg.name AS FileGroupName,

prv_left.value AS LowerBoundaryValue,

prv_right.value AS UpperBoundaryValue,

CASE pf.boundary_value_on_right

WHEN 1 THEN 'RIGHT'

ELSE 'LEFT'

END AS Range,

p.rows AS Rows

FROM sys.partitions AS p

JOIN sys.indexes AS i ON i.object_id = p.object_id

AND i.index_id = p.index_id

JOIN sys.data_spaces AS ds ON ds.data_space_id = i.data_space_id

JOIN sys.partition_schemes AS ps ON ps.data_space_id = ds.data_space_id

JOIN sys.partition_functions AS pf ON pf.function_id = ps.function_id

JOIN sys.destination_data_spaces AS dds2 ON dds2.partition_scheme_id = ps.data_space_id

AND dds2.destination_id = p.partition_number

JOIN sys.filegroups AS fg ON fg.data_space_id = dds2.data_space_id

LEFT JOIN sys.partition_range_values AS prv_left ON ps.function_id = prv_left.function_id

AND prv_left.boundary_id = p.partition_number - 1

LEFT JOIN sys.partition_range_values AS prv_right ON ps.function_id = prv_right.function_id

AND prv_right.boundary_id = p.partition_number

WHERE OBJECTPROPERTY(p.object_id, 'ISMSShipped') = 0

UNION ALL

--non-partitioned table/indexes

SELECT OBJECT_NAME(p.object_id) AS ObjectName,

i.name AS IndexName,

p.index_id AS IndexID,

NULL AS PartitionScheme,

p.partition_number AS PartitionNumber,

fg.name AS FileGroupName,

NULL AS LowerBoundaryValue,

NULL AS UpperBoundaryValue,

NULL AS Boundary,

p.rows AS Rows

FROM sys.partitions AS p

JOIN sys.indexes AS i ON i.object_id = p.object_id

AND i.index_id = p.index_id

JOIN sys.data_spaces AS ds ON ds.data_space_id = i.data_space_id

JOIN sys.filegroups AS fg ON fg.data_space_id = i.data_space_id

WHERE OBJECTPROPERTY(p.object_id, 'ISMSShipped') = 0

ORDER BY ObjectName,

IndexID,

PartitionNumber;

Notice that the source is a subset of the destination but the converse is not true. Since the partition swap is a DDL operation no data is evaluated to see if the data actually could conform to the boundary, it just says yes or no based on the metadata.